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new sistem

Topic closed. 7 replies. Last post 1 year ago by dr san.

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bgonçalves
Brasil
Member #92566
June 9, 2010
1362 Posts
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Posted: January 21, 2013, 1:52 pm - IP Logged

Let us take events of a lottery of daily draw. Let the following numbers be the results of daily draw of a single digit lottery

1, 5, 8, 3, 6, 7. ……… If you look at the numbers, you will find that the events are totally at random in occurrence and absolutely with no relevance in between them. You cannot predict the next lottery number however expert you may be in statistics. There is a total uncertainty in forecasting next number. The BEST method in forecasting the next event is ‘conditional probability method ‘. In this method, another parallel format of  event  for each occurrence of numbers is taken in account and future event is predicted against the occurrence of the number in the conditional format. This method is known as ‘linear regression method ‘ In simple terms predicting the future value by using existing values. The predicted value is a Y value for a given X value.  The known values are existing x-values and y-values, and the new value is predicted by using linear regression. You can use this function to predict future sales, inventory requirements, or consumer trends, in forecasting gambling, horse racing and many more. Given below are STEPS, which will make you to understand the NEW CONCEPT and how to use it in forecasting future events without much fuss and in utmost probability levels.

 

 

 

                                                            STEP -1                                 

 

                                                                                                                                               

Select some random variable serial wise and lay those in a column K as below and in the left side column are alphabets denoting the corresponding integer on the right side. Let us select six random variables.

                                                            STEP - 2

 

 

 

 

Subtract the lower integer from the top integer of column K  and display the results in the next column as shown below. The procedure goes as 1 – 5 ( A – B ) = - 4,  5 – 8 ( B – C ) =  - 3,  ….. so on. Continue this procedure until you get single cell display at the end, as shown in figure 2.

 

 

 

 

 

 

                  Figure – 1                                                  Figure - 2

 

    # K

 

 

 

 

 

A

1

 

 

 

 

 

B

5

-4

 

 

 

 

C

8

-3

-1

 

 

 

D

3

5

-8

7

 

 

E

6

-3

8

-16

23

 

F

7

-1

-2

10

-26

49

 

    K

 

A

1

 

  B

5

-4

C

8

-3

D

3

5

E

6

-3

F

7

-1

                                               

 

 

 

  End nos.

  ( brown color)

 

       

  End cell

 

                                      ( End nos. or end cells are shown as brown with end cell)

                                                   

In evolving further procedure, we will take the example of figure – 2 and displayed as below.                                                                                       

                                                                                               

 

 

 

 

this row contains  integers selected at random

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  A

 

 

 

 

 

 

 

# A

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A

1

 

 

 

 

 

 

 

1

f

 

 

B

5

-4

 

 

 

 

 

 

1

 

 

 

C

8

-3

-1

 

 

 

 

 

4

-3

 

 

D

3

5

-8

7

 

 

 

 

7

-3

 

 

E

6

-3

8

-16

23

 

 

 

18

-11

8

 

F

7

-1

-2

10

-26

49

 

 

37

-19

8

0

                                                                                                Formatted triangle - above

 

 

 

                                                      STEP – 3

 

 

 

 

Add all the numbers of each row and display it in the column # A shown as above as

 

In row A = 1 + 0 = 1, in row B =  5 + ( - 4 )  = 1,  in row C = 8 + ( - 3 ) + ( - 1 ) = 4………so on

 

Continue this process till you gets a format on the left side and I call it as FORMATTED TRIANGLE and the first column as FORMATTED COLUMN or as # A  (brown in color)

 

 

 

 

                                                      STEP - 4

 

 

 

 

The formatted triangle, as mentioned above is the main fundamental feature of the formatting  and in the coming lines many interesting properties or you can say as interesting FEATURES are found in the FORMATTED TRIANGLE. Now we shall proceed further in evolving many interesting

 

 

 

 

features that the formatted triangle contains. Let us first take the formatted triangle, shown as above

 

Feature1). The top two digits, A & B will be same in value

 

 

 

 

Feature no. 2). The difference of third integer from 2nd, and 4th  to 3rd will

 

  - be same. B – C = C – D, as seen in the next column as -3, -3

 

1

 

 

 

1     

 

 

 

4

-3

 

 

  7

-3

 

 

18

-11

8

 

37

-19

8

0

 

 

 

Feature no. 3) the next integers, E & F will have the same difference when evolved further, seen as – 8, - 8.

 

This is one fundamental property of formatted property and

 

 

 

@ true to all formatted triangle formations for any given population of column of random nos.  A. shown in STEP-2

 

 

 

                                                          STEP -5

 

 

 

 

Here go the real action of explorations. The formatted triangle as worked out above is to be taken into account as many of interesting features could be found in evolving the formatted triangle further, as below.

 

 

 

 

#  A

 

 

 

 

 

 

A

1

 

 

 

 

 

 

B

1

0

 

 

 

 

 

C

4

-3

3

 

 

 

 

D

7

-3

0

3

 

 

 

E

18

-11

8

-8

11

 

 

F

37

-19

8

0

-8

19

 

 

 

 

 

 

 

A

1

 

 

 

B

1

0

 

 

C

4

-3

 

 

D

7

-3

0

 

E

18

-11

8

0

F

37

-19

8

0

 

 

 

                                                                       

 

 

Figure - 2

 

 

 

                              Figure – 1                                               

                  (  Formatted triangle)

 

 

 

Figure – 1 is formatted triangle as described above. When the digits displayed in the column # A is again further formatted, as shown in figure – 2, the same replica of  figure – 1 is seen . That is say that the totals of each row of triangle in figure – 1, will be same as of column # A. If you take the examples in STEP-2, the formatted triangle displayed in Figure -2  is not the replica of

Figure - 1

Feature no 4) The first column # A of formatted triangle is again formatted, it will be the same replica of the first triangle.

 

 

 

 

Take the integers of column # A from figure – 1 as shown above and the end integers of same row. The display will be as below. Subtract the end nos. from column # A and observe the result.

 

 

 

 

 

# A            end nos        #A – end nos.

1 

 

1

1

 

0

4

 

3

7

 

3

18

 

11

37

 

19

0

1

1

4

7

18

The figures in this column is the result of #A – end nos.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  #A            RND                         

1   

1

4

7

18

37

1

5

8

3

6

7

                                                                                                     

  Subtract column RND from column #A and the result will be as                             

Displayed as below and

  Feature no 6) There is a conditional correlation between the original   Random nos. and its’ formatted sequences

  as seen in the extreme right column  wherein the differences

between  the consecutive cells are displayed.                                                     

                                                   

0

 

-4

 

-4

0

4

0

12

-8

30

-18

 

 

 

 

 For next feature , let us take  the formatted olumn #A  and include ‘ 0 ‘ on the top cell as shown below  and repeat the formatting as explained in STEP -2, figure – 2.

 

 

        #A        Zero start format

 

0

 

 

 

 

 

 

 

  1

-1

 

 

 

 

 

1

0

-1

 

 

 

 

4

-3

3

-4

 

 

 

7

-3

0

3

-7

 

 

18

-11

8

-8

11

-18

 

37

-19

8

0

-8

19

-37

 

 

 

 

 

 

 

 

 

 

 

0

 

 

 

 0

 0

 0

 0

 0

0

0

 

Feature no 7) The totals of all the consecutive rows will always be equal to ‘ 0 ‘ as

seen in the right side column. Feature no 8) The first cell and the consecutive

  cells running in diagonal format in the next row will always = 0.

 

 

 

 

 It can be seen from the above example that how the feature of display of ‘ 0 ‘  will be continuing diagonally in all the cells falling diagonally in the next consecutive rows and can be extended further to any length and displaying the totals of row integers as = 0 up to the last row.

Feature no 9) Below each cell, staring with the first cell with ‘ 0 ‘ display and its’ diagonal cells with ‘ 0 ‘ displays in the consecutive rows will always have formatted conditional sequences. Let us observe the first column. You will find with ‘ 0 ‘ on top cell  and sequence below cells are conditional formats repeated in the next columns below each cell with ‘ 0 ‘ falling in the diagonal path for any extension.

Feature no 10) The end nos. of each row will always have same value in negative as of the first nos. of the same row as seen in the above example, the last integer and the first integer of a row, are same but opposite and their totals will always = 0

                                                                        STEP – 6

 

In this section we will elaborate some more interesting features.

For next feature, let us take the original random variable example as shown in STEP – 2, as displayed below

           A                                                                                   A         end nos.               

1

 

 

 

 

 

  5

-4

 

 

 

 

8

-3

-1

 

 

 

3

5

-8

7

 

     

6

-3

8

-16

23

 

7

-1

-2

10

-26

49

            1              1                      2
             5             -4                     1 
              8            -1                     7
              3              7                   10
              6             23                  29
              7             49                 56
 In the above example, the column is the display of original random variables selected and the subsequent columns are the display of column A, the end nos. and last one is the total of col. A and the end nos. of each row. Let us take the column of the ‘total’ for further evolution and exploring new features as below.

Now we will triangle format the total column as explained in STEP – 2

total

2

 

 

 

 

 

1

1

 

 

 

 

7

-6

7

 

 

 

10

-3

-3

10

 

 

29

-19

16

-19

29

 

56

-27

8

8

-27

56

Feature no 11) The differences between the integers and the subsequent end nos. of

 

  each row will be of same value. In this example the

  difference found is = 0( not necessarily =0 and can be of any value)

 

 

 

 

 

 

 

 

 

In continuation for some more features, let us take the original random variables as shown in STEP – 2. Take the end nos. ( in boxes) of each row of  format – 1, and display them in  the first column of format – 2, as below

 

                Format - 1                                                            format - 2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

 

 

 

 

1

 

 

 

 

 

 

5

-4

 

 

 

 

 

-4

5

 

 

 

 

 

8

-3

-1

 

 

 

 

-1

-3

8

 

 

 

 

3

5

-8

7

 

 

 

 

7

-8

5

3

 

 

 

6

-3

8

-16

23

 

 

 

23

-16

8

-3

6

 

 

7

-1

-2

10

-26

49

 

 

49

-26

10

-2

-1

7

 

 

 

 

 

 Feature no 12) The integers of first column of format – 1 are formed as end nos. of format -2 and the integers of end nos. of format -1 are formed in the first column of format -2 and vice versa.

 

                                                              STEP – 7

 

 

 

 

Till now we have taken only six random variables for triangle formatting. We shall go further in selecting more random variables for exploring some more features and verifications. Let us take ten random variables in series triangle format it as described in  STEP – 2.

 

 

 

A

 

 

 

 

 

 

 

 

 

 

5

 

 

 

 

 

 

 

 

 

5

7

-2

 

 

 

 

 

 

 

 

5

4

3

-5

 

 

 

 

 

 

 

2

0

4

-1

-4

 

 

 

 

 

 

-1

5

-5

9

-10

6

 

 

 

 

 

5

7

-2

-3

12

-22

28

 

 

 

 

20

2

5

-7

4

8

-30

58

 

 

 

40

7

-5

10

-17

21

-13

-17

75

 

 

61

1

6

-11

21

-38

59

-72

55

20

 

41

6

-5

11

-22

43

-81

140

-212

267

-247

-100

 

Take the formatted column #A and display it as below denoting each cell with alphabetic letters on the left side.

 

 

                                              VIEW - 2

 

A

B

C

D

E

F

G

H

I

J

  #A

5

5

2

-1

5

20

40

61

41

-100

 

 

 

 

 

 

 

  =

A

 

 

 

 

 

  =

A

 

 

 

 

 

  =

A -B +C

 

 

 

 

  =

A-2B+2C

 

 

 

 

  =

A-3B+4C-2D+E

 

 

 

  =

A-4B+7C-6D+3E

 

 

 

  =

A-5B+11C-13D+9E-3F+G

 

 

  =

A-6B  +16C-24D+22E-12F+4G

 

  =

A-7B+22C-40D+46E-34F+16G-4H+I

  =

A-8B+29C-62D+86E-80F+50G-20H+5I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Feature no. 12). The formation of column #A can be calculated by formulas as described on the right side format without doing for real time triangle formatting as of VIEW - 1

  Feature no) 13). Periodicity of alphabetical order is seen in the order of formulas.

If you look at the formulas,  VIEW – 2, the periodicity of display order is seen as column wise as A, A, A, A, …….B, 2B, 3B, 4C, ……..C, 2C, 4C, 7C, 11C, ….and so on

 

 

 

The formatted column #A, some more fundamental properties numbering 14, 15, 16, & 17) and the formulas may be of much helpful in many statistical applications.

 

 

 

 

 

 

 

 

 

 

 

Examples

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  14)

B-2C+D  = 0

 

 

 

5 - 2*2 +  ( -1 ) = 0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  15)

C-3D+3E-F  = 0

 

 

2 - ( -1  )*3 + 5*3 - 20 = 0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  16)

D-4E +  6F - 4G + H = 0

 

( -1 ) -   (5 )*4 + 20*6 - 40*4 + 61 = 0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  17)

E - 5F  +10G - 10H + 5I - J = 0

5 -   (20)*5 + 40*10 - 61*10 + 41*5 - 100 = 0

 

 

 

Feature no18) Periodicity of alphabetical order is also seen in the display of above formulasas described in feature no 13). In evolving further such features in bigger populations, computer application is needed to identify such equations as described above and also it is a matter of working this new concept on the computer surely many of similar more features could be found with the help of the computer in working with large population of data. 

 

                                                          STEP – 8

 

 

 Before going further, it is important to understand the above concepts and the said features by working with different small samples on paper, preferably on Microsoft Excel work sheet on computer and test the features.

 

USE OF THE NEW CONCEPT IN PROBABILITY, FORECAST 

 

How this concept can be incorporated in evaluating probability & forecast, particularly when the population contains random and uncertainty level ? let us take some examples and work out implementing some of the said features. Sample 1s taken from STEP -7, WIEW – 1.

                 

 

A

 

 

 

 

 

 

 

 

 

  #A

A

5

 

 

 

 

 

 

 

 

 

5

B

7

-2

 

 

 

 

 

 

 

 

5

C

4

3

-5

 

 

 

 

 

 

 

2

D

0

4

-1

-4

 

 

 

 

 

 

-1

E

5

-5

9

-10

6

 

 

 

 

 

5

F

7

-2

-3

12

-22

28

 

 

 

 

20

G

2

5

-7

4

8

-30

58

 

 

 

40

H

7

-5

10

-17

21

-13

-17

75

 

 

61

I

1

6

-11

21

-38

59

-72

55

20

 

41

J

6

-5

11

-22

43

-81

140

-212

267

-247

-100

           

                  The numbers displayed in the column A is selected randomly and triangle formatted as described in STEP – 2. 

The numbers displayed in #A column are formatted by adding integers on the left format row wise. As said that the two columns A  &  #A will have conditional probability, we will take the two columns separately and work out.                             

 

 

 

 

 

 

    #A

A

 

M

A

5

5

 

0

B

5

7

 

-2

C

2

4

 

-2

D

-1

0

 

-1

E

5

5

 

0

F

20

7

 

13

G

40

2

 

38

H

61

7

 

54

I

41

1

 

40

J

-100

X

 

- X - 100

  In the column M, the results are displayed as col. #A – A. for the sake of calculations, the last cell of column A is denoted with ‘ X ‘ as to forecast the event in the population of nine selected events selected randomly as displayed in column A. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

As described in the earlier features, a conditional probability is seen between the two columns #A and A. the nos. in the column M will fall in the line with conditional probability of #A in all respects. In Linear Progression methods, forecast is evaluated with two set of serial nos.. one is conditional with known nos. & the other is un conditional. With un known nos. Here col. A is unconditional and #A is conditional and  forecast of  X can be evaluated against the known number ( - 100 ), using the Linear Regression method or better with Monte Carlo simulation applications. How you are going to evaluate the number ( - 100 ) in column #A ? by using the formula

A-8B+29C-62D+86E-80F+50G-20H+5I = J = - 100

 

 

 

 

If  letters are substituted with integers of corresponding cells, the total will be =  - 100

The easy way is to look in the 9th row ( I row ), add up the 1, 3, 5, 7 and 9th cells  

Important :-  the selection of the random variables must always be ODD in number 

 

There are several ways in selecting the proper conditional serial format with column A

1). The column can be selected with any formatted column, arising there by after triangle formatting the column A as described in many examples in the above STEPS. in this way you get many options of conditional formatted series in evaluating the forest of X to a greater level of accuracy. Some times all or majority of cells in #A will coincide with the corresponding cells of column A.

2). As the column #A is formatted one with unknown event in the last column as              ( - 1 - 100 ). And the above cells are known & conditional with well defined periodicity, the forecasting the last event can well be evolved with many applications of statistical analysis, most preferably with Monte Carlo simulations.

3). The features of 14),  15).  16),  &  17) with formulas having well defined periodicity,  and the Zero start format, described in STEP – 5,  are very useful in evaluating the propagation of future trails in the conditional series.

 

                                                        STEP -  9 

 

. There are several features hidden in the formatted columns like that of #A. we will explore some of the unique features by formatting the #A in different way.

Example taken is column #A. as below.

 

 

 

 

1st.col

2nd.col

3rd.col

4th,col

5th.col

6th.col

 

The procedure goes as

 

 

 

  #A

 

 

 

 

 

 

2nd col.:- A+B-C = 8.  B+C-A = 8.

A

5

 

 

 

 

 

 

 

C+D-E = - 4…….. So on

 

B

5

 

 

 

 

 

 

 

 

 

 

 

 

C

2

8

 

 

 

 

 

Continue the process to 6th column

D

-1

8

 

 

 

 

 

 

 

 

 

 

 

E

5

-4

20

 

 

 

 

 

 

 

 

 

 

F

20

-16

20

 

 

 

 

 

 

 

 

 

 

G

40

-15

-5

45

 

 

 

 

 

 

 

 

 

H

61

-1

-30

45

 

 

 

 

 

 

 

 

 

I

41

60

-76

41

49

 

 

 

 

 

 

 

 

J

-100

202

-143

37

49

0

 

 

 

 

 

 

 

 

 

 

In the above example it can be seen that several well defined formatted columns could be generated from single column #A. larger the integers in col. #A. larger will be the generated # columns. If the last cell of col. #A is substituted with variable X. all the end cells of each subsequent columns will have different values with X+ or X- .

Important : - in selecting any two columns in forecasting applications, the top two paired nos. in the columns should be lined in a row. 

 

In conclusion, there are many such features that somebody can explore by using the computes and by selecting large populations. May be, some of the features thus found  are more interesting and more potent in the applications of many probability forecasts.

 

 

 

 

 

 

 

 

 

 

 

 

 

Search Engine Submission - AddMe

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    lakerben's avatar - Lottery-027.jpg
    New Mexico
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    Member #86100
    January 29, 2010
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    Posted: January 21, 2013, 3:59 pm - IP Logged

    Let us take events of a lottery of daily draw. Let the following numbers be the results of daily draw of a single digit lottery

    1, 5, 8, 3, 6, 7. ……… If you look at the numbers, you will find that the events are totally at random in occurrence and absolutely with no relevance in between them. You cannot predict the next lottery number however expert you may be in statistics. There is a total uncertainty in forecasting next number. The BEST method in forecasting the next event is ‘conditional probability method ‘. In this method, another parallel format of  event  for each occurrence of numbers is taken in account and future event is predicted against the occurrence of the number in the conditional format. This method is known as ‘linear regression method ‘ In simple terms predicting the future value by using existing values. The predicted value is a Y value for a given X value.  The known values are existing x-values and y-values, and the new value is predicted by using linear regression. You can use this function to predict future sales, inventory requirements, or consumer trends, in forecasting gambling, horse racing and many more. Given below are STEPS, which will make you to understand the NEW CONCEPT and how to use it in forecasting future events without much fuss and in utmost probability levels.

     

     

     

                                                                STEP -1                                 

     

                                                                                                                                                   

    Select some random variable serial wise and lay those in a column K as below and in the left side column are alphabets denoting the corresponding integer on the right side. Let us select six random variables.

                                                                STEP - 2

     

     

     

     

    Subtract the lower integer from the top integer of column K  and display the results in the next column as shown below. The procedure goes as 1 – 5 ( A – B ) = - 4,  5 – 8 ( B – C ) =  - 3,  ….. so on. Continue this procedure until you get single cell display at the end, as shown in figure 2.

     

     

     

     

     

     

                      Figure – 1                                                  Figure - 2

     

        # K

     

     

     

     

     

    A

    1

     

     

     

     

     

    B

    5

    -4

     

     

     

     

    C

    8

    -3

    -1

     

     

     

    D

    3

    5

    -8

    7

     

     

    E

    6

    -3

    8

    -16

    23

     

    F

    7

    -1

    -2

    10

    -26

    49

     

        K

     

    A

    1

     

      B

    5

    -4

    C

    8

    -3

    D

    3

    5

    E

    6

    -3

    F

    7

    -1

                                                   

     

     

     

      End nos.

      ( brown color)

     

           

      End cell

     

                                          ( End nos. or end cells are shown as brown with end cell)

                                                       

    In evolving further procedure, we will take the example of figure – 2 and displayed as below.                                                                                       

                                                                                                   

     

     

     

     

    this row contains  integers selected at random

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

      A

     

     

     

     

     

     

     

    # A

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

    A

    1

     

     

     

     

     

     

     

    1

    f

     

     

    B

    5

    -4

     

     

     

     

     

     

    1

     

     

     

    C

    8

    -3

    -1

     

     

     

     

     

    4

    -3

     

     

    D

    3

    5

    -8

    7

     

     

     

     

    7

    -3

     

     

    E

    6

    -3

    8

    -16

    23

     

     

     

    18

    -11

    8

     

    F

    7

    -1

    -2

    10

    -26

    49

     

     

    37

    -19

    8

    0

                                                                                                    Formatted triangle - above

     

     

     

                                                          STEP – 3

     

     

     

     

    Add all the numbers of each row and display it in the column # A shown as above as

     

    In row A = 1 + 0 = 1, in row B =  5 + ( - 4 )  = 1,  in row C = 8 + ( - 3 ) + ( - 1 ) = 4………so on

     

    Continue this process till you gets a format on the left side and I call it as FORMATTED TRIANGLE and the first column as FORMATTED COLUMN or as # A  (brown in color)

     

     

     

     

                                                          STEP - 4

     

     

     

     

    The formatted triangle, as mentioned above is the main fundamental feature of the formatting  and in the coming lines many interesting properties or you can say as interesting FEATURES are found in the FORMATTED TRIANGLE. Now we shall proceed further in evolving many interesting

     

     

     

     

    features that the formatted triangle contains. Let us first take the formatted triangle, shown as above

     

    Feature1). The top two digits, A & B will be same in value

     

     

     

     

    Feature no. 2). The difference of third integer from 2nd, and 4th  to 3rd will

     

      - be same. B – C = C – D, as seen in the next column as -3, -3

     

    1

     

     

     

    1     

     

     

     

    4

    -3

     

     

      7

    -3

     

     

    18

    -11

    8

     

    37

    -19

    8

    0

     

     

     

    Feature no. 3) the next integers, E & F will have the same difference when evolved further, seen as – 8, - 8.

     

    This is one fundamental property of formatted property and

     

     

     

    @ true to all formatted triangle formations for any given population of column of random nos.  A. shown in STEP-2

     

     

     

                                                              STEP -5

     

     

     

     

    Here go the real action of explorations. The formatted triangle as worked out above is to be taken into account as many of interesting features could be found in evolving the formatted triangle further, as below.

     

     

     

     

    #  A

     

     

     

     

     

     

    A

    1

     

     

     

     

     

     

    B

    1

    0

     

     

     

     

     

    C

    4

    -3

    3

     

     

     

     

    D

    7

    -3

    0

    3

     

     

     

    E

    18

    -11

    8

    -8

    11

     

     

    F

    37

    -19

    8

    0

    -8

    19

     

     

     

     

     

     

     

    A

    1

     

     

     

    B

    1

    0

     

     

    C

    4

    -3

     

     

    D

    7

    -3

    0

     

    E

    18

    -11

    8

    0

    F

    37

    -19

    8

    0

     

     

     

                                                                           

     

     

    Figure - 2

     

     

     

                                  Figure – 1                                               

                      (  Formatted triangle)

     

     

     

    Figure – 1 is formatted triangle as described above. When the digits displayed in the column # A is again further formatted, as shown in figure – 2, the same replica of  figure – 1 is seen . That is say that the totals of each row of triangle in figure – 1, will be same as of column # A. If you take the examples in STEP-2, the formatted triangle displayed in Figure -2  is not the replica of

    Figure - 1

    Feature no 4) The first column # A of formatted triangle is again formatted, it will be the same replica of the first triangle.

     

     

     

     

    Take the integers of column # A from figure – 1 as shown above and the end integers of same row. The display will be as below. Subtract the end nos. from column # A and observe the result.

     

     

     

     

     

    # A            end nos        #A – end nos.

    1 

     

    1

    1

     

    0

    4

     

    3

    7

     

    3

    18

     

    11

    37

     

    19

    0

    1

    1

    4

    7

    18

    The figures in this column is the result of #A – end nos.

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

      #A            RND                         

    1   

    1

    4

    7

    18

    37

    1

    5

    8

    3

    6

    7

                                                                                                         

      Subtract column RND from column #A and the result will be as                             

    Displayed as below and

      Feature no 6) There is a conditional correlation between the original   Random nos. and its’ formatted sequences

      as seen in the extreme right column  wherein the differences

    between  the consecutive cells are displayed.                                                     

                                                       

    0

     

    -4

     

    -4

    0

    4

    0

    12

    -8

    30

    -18

     

     

     

     

     For next feature , let us take  the formatted olumn #A  and include ‘ 0 ‘ on the top cell as shown below  and repeat the formatting as explained in STEP -2, figure – 2.

     

     

            #A        Zero start format

     

    0

     

     

     

     

     

     

     

      1

    -1

     

     

     

     

     

    1

    0

    -1

     

     

     

     

    4

    -3

    3

    -4

     

     

     

    7

    -3

    0

    3

    -7

     

     

    18

    -11

    8

    -8

    11

    -18

     

    37

    -19

    8

    0

    -8

    19

    -37

     

     

     

     

     

     

     

     

     

     

     

    0

     

     

     

     0

     0

     0

     0

     0

    0

    0

     

    Feature no 7) The totals of all the consecutive rows will always be equal to ‘ 0 ‘ as

    seen in the right side column. Feature no 8) The first cell and the consecutive

      cells running in diagonal format in the next row will always = 0.

     

     

     

     

     It can be seen from the above example that how the feature of display of ‘ 0 ‘  will be continuing diagonally in all the cells falling diagonally in the next consecutive rows and can be extended further to any length and displaying the totals of row integers as = 0 up to the last row.

    Feature no 9) Below each cell, staring with the first cell with ‘ 0 ‘ display and its’ diagonal cells with ‘ 0 ‘ displays in the consecutive rows will always have formatted conditional sequences. Let us observe the first column. You will find with ‘ 0 ‘ on top cell  and sequence below cells are conditional formats repeated in the next columns below each cell with ‘ 0 ‘ falling in the diagonal path for any extension.

    Feature no 10) The end nos. of each row will always have same value in negative as of the first nos. of the same row as seen in the above example, the last integer and the first integer of a row, are same but opposite and their totals will always = 0

                                                                            STEP – 6

     

    In this section we will elaborate some more interesting features.

    For next feature, let us take the original random variable example as shown in STEP – 2, as displayed below

               A                                                                                   A         end nos.               

    1

     

     

     

     

     

      5

    -4

     

     

     

     

    8

    -3

    -1

     

     

     

    3

    5

    -8

    7

     

         

    6

    -3

    8

    -16

    23

     

    7

    -1

    -2

    10

    -26

    49

                1              1                      2
                 5             -4                     1 
                  8            -1                     7
                  3              7                   10
                  6             23                  29
                  7             49                 56
     In the above example, the column is the display of original random variables selected and the subsequent columns are the display of column A, the end nos. and last one is the total of col. A and the end nos. of each row. Let us take the column of the ‘total’ for further evolution and exploring new features as below.

    Now we will triangle format the total column as explained in STEP – 2

    total

    2

     

     

     

     

     

    1

    1

     

     

     

     

    7

    -6

    7

     

     

     

    10

    -3

    -3

    10

     

     

    29

    -19

    16

    -19

    29

     

    56

    -27

    8

    8

    -27

    56

    Feature no 11) The differences between the integers and the subsequent end nos. of

     

      each row will be of same value. In this example the

      difference found is = 0( not necessarily =0 and can be of any value)

     

     

     

     

     

     

     

     

     

    In continuation for some more features, let us take the original random variables as shown in STEP – 2. Take the end nos. ( in boxes) of each row of  format – 1, and display them in  the first column of format – 2, as below

     

                    Format - 1                                                            format - 2

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

    1

     

     

     

     

     

     

     

    1

     

     

     

     

     

     

    5

    -4

     

     

     

     

     

    -4

    5

     

     

     

     

     

    8

    -3

    -1

     

     

     

     

    -1

    -3

    8

     

     

     

     

    3

    5

    -8

    7

     

     

     

     

    7

    -8

    5

    3

     

     

     

    6

    -3

    8

    -16

    23

     

     

     

    23

    -16

    8

    -3

    6

     

     

    7

    -1

    -2

    10

    -26

    49

     

     

    49

    -26

    10

    -2

    -1

    7

     

     

     

     

     

     Feature no 12) The integers of first column of format – 1 are formed as end nos. of format -2 and the integers of end nos. of format -1 are formed in the first column of format -2 and vice versa.

     

                                                                  STEP – 7

     

     

     

     

    Till now we have taken only six random variables for triangle formatting. We shall go further in selecting more random variables for exploring some more features and verifications. Let us take ten random variables in series triangle format it as described in  STEP – 2.

     

     

     

    A

     

     

     

     

     

     

     

     

     

     

    5

     

     

     

     

     

     

     

     

     

    5

    7

    -2

     

     

     

     

     

     

     

     

    5

    4

    3

    -5

     

     

     

     

     

     

     

    2

    0

    4

    -1

    -4

     

     

     

     

     

     

    -1

    5

    -5

    9

    -10

    6

     

     

     

     

     

    5

    7

    -2

    -3

    12

    -22

    28

     

     

     

     

    20

    2

    5

    -7

    4

    8

    -30

    58

     

     

     

    40

    7

    -5

    10

    -17

    21

    -13

    -17

    75

     

     

    61

    1

    6

    -11

    21

    -38

    59

    -72

    55

    20

     

    41

    6

    -5

    11

    -22

    43

    -81

    140

    -212

    267

    -247

    -100

     

    Take the formatted column #A and display it as below denoting each cell with alphabetic letters on the left side.

     

     

                                                  VIEW - 2

     

    A

    B

    C

    D

    E

    F

    G

    H

    I

    J

      #A

    5

    5

    2

    -1

    5

    20

    40

    61

    41

    -100

     

     

     

     

     

     

     

      =

    A

     

     

     

     

     

      =

    A

     

     

     

     

     

      =

    A -B +C

     

     

     

     

      =

    A-2B+2C

     

     

     

     

      =

    A-3B+4C-2D+E

     

     

     

      =

    A-4B+7C-6D+3E

     

     

     

      =

    A-5B+11C-13D+9E-3F+G

     

     

      =

    A-6B  +16C-24D+22E-12F+4G

     

      =

    A-7B+22C-40D+46E-34F+16G-4H+I

      =

    A-8B+29C-62D+86E-80F+50G-20H+5I

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

    Feature no. 12). The formation of column #A can be calculated by formulas as described on the right side format without doing for real time triangle formatting as of VIEW - 1

      Feature no) 13). Periodicity of alphabetical order is seen in the order of formulas.

    If you look at the formulas,  VIEW – 2, the periodicity of display order is seen as column wise as A, A, A, A, …….B, 2B, 3B, 4C, ……..C, 2C, 4C, 7C, 11C, ….and so on

     

     

     

    The formatted column #A, some more fundamental properties numbering 14, 15, 16, & 17) and the formulas may be of much helpful in many statistical applications.

     

     

     

     

     

     

     

     

     

     

     

    Examples

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

      14)

    B-2C+D  = 0

     

     

     

    5 - 2*2 +  ( -1 ) = 0

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

      15)

    C-3D+3E-F  = 0

     

     

    2 - ( -1  )*3 + 5*3 - 20 = 0

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

      16)

    D-4E +  6F - 4G + H = 0

     

    ( -1 ) -   (5 )*4 + 20*6 - 40*4 + 61 = 0

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

      17)

    E - 5F  +10G - 10H + 5I - J = 0

    5 -   (20)*5 + 40*10 - 61*10 + 41*5 - 100 = 0

     

     

     

    Feature no18) Periodicity of alphabetical order is also seen in the display of above formulasas described in feature no 13). In evolving further such features in bigger populations, computer application is needed to identify such equations as described above and also it is a matter of working this new concept on the computer surely many of similar more features could be found with the help of the computer in working with large population of data. 

     

                                                              STEP – 8

     

     

     Before going further, it is important to understand the above concepts and the said features by working with different small samples on paper, preferably on Microsoft Excel work sheet on computer and test the features.

     

    USE OF THE NEW CONCEPT IN PROBABILITY, FORECAST 

     

    How this concept can be incorporated in evaluating probability & forecast, particularly when the population contains random and uncertainty level ? let us take some examples and work out implementing some of the said features. Sample 1s taken from STEP -7, WIEW – 1.

                     

     

    A

     

     

     

     

     

     

     

     

     

      #A

    A

    5

     

     

     

     

     

     

     

     

     

    5

    B

    7

    -2

     

     

     

     

     

     

     

     

    5

    C

    4

    3

    -5

     

     

     

     

     

     

     

    2

    D

    0

    4

    -1

    -4

     

     

     

     

     

     

    -1

    E

    5

    -5

    9

    -10

    6

     

     

     

     

     

    5

    F

    7

    -2

    -3

    12

    -22

    28

     

     

     

     

    20

    G

    2

    5

    -7

    4

    8

    -30

    58

     

     

     

    40

    H

    7

    -5

    10

    -17

    21

    -13

    -17

    75

     

     

    61

    I

    1

    6

    -11

    21

    -38

    59

    -72

    55

    20

     

    41

    J

    6

    -5

    11

    -22

    43

    -81

    140

    -212

    267

    -247

    -100

               

                      The numbers displayed in the column A is selected randomly and triangle formatted as described in STEP – 2. 

    The numbers displayed in #A column are formatted by adding integers on the left format row wise. As said that the two columns A  &  #A will have conditional probability, we will take the two columns separately and work out.                             

     

     

     

     

     

     

        #A

    A

     

    M

    A

    5

    5

     

    0

    B

    5

    7

     

    -2

    C

    2

    4

     

    -2

    D

    -1

    0

     

    -1

    E

    5

    5

     

    0

    F

    20

    7

     

    13

    G

    40

    2

     

    38

    H

    61

    7

     

    54

    I

    41

    1

     

    40

    J

    -100

    X

     

    - X - 100

      In the column M, the results are displayed as col. #A – A. for the sake of calculations, the last cell of column A is denoted with ‘ X ‘ as to forecast the event in the population of nine selected events selected randomly as displayed in column A. 

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

    As described in the earlier features, a conditional probability is seen between the two columns #A and A. the nos. in the column M will fall in the line with conditional probability of #A in all respects. In Linear Progression methods, forecast is evaluated with two set of serial nos.. one is conditional with known nos. & the other is un conditional. With un known nos. Here col. A is unconditional and #A is conditional and  forecast of  X can be evaluated against the known number ( - 100 ), using the Linear Regression method or better with Monte Carlo simulation applications. How you are going to evaluate the number ( - 100 ) in column #A ? by using the formula

    A-8B+29C-62D+86E-80F+50G-20H+5I = J = - 100

     

     

     

     

    If  letters are substituted with integers of corresponding cells, the total will be =  - 100

    The easy way is to look in the 9th row ( I row ), add up the 1, 3, 5, 7 and 9th cells  

    Important :-  the selection of the random variables must always be ODD in number 

     

    There are several ways in selecting the proper conditional serial format with column A

    1). The column can be selected with any formatted column, arising there by after triangle formatting the column A as described in many examples in the above STEPS. in this way you get many options of conditional formatted series in evaluating the forest of X to a greater level of accuracy. Some times all or majority of cells in #A will coincide with the corresponding cells of column A.

    2). As the column #A is formatted one with unknown event in the last column as              ( - 1 - 100 ). And the above cells are known & conditional with well defined periodicity, the forecasting the last event can well be evolved with many applications of statistical analysis, most preferably with Monte Carlo simulations.

    3). The features of 14),  15).  16),  &  17) with formulas having well defined periodicity,  and the Zero start format, described in STEP – 5,  are very useful in evaluating the propagation of future trails in the conditional series.

     

                                                            STEP -  9 

     

    . There are several features hidden in the formatted columns like that of #A. we will explore some of the unique features by formatting the #A in different way.

    Example taken is column #A. as below.

     

     

     

     

    1st.col

    2nd.col

    3rd.col

    4th,col

    5th.col

    6th.col

     

    The procedure goes as

     

     

     

      #A

     

     

     

     

     

     

    2nd col.:- A+B-C = 8.  B+C-A = 8.

    A

    5

     

     

     

     

     

     

     

    C+D-E = - 4…….. So on

     

    B

    5

     

     

     

     

     

     

     

     

     

     

     

     

    C

    2

    8

     

     

     

     

     

    Continue the process to 6th column

    D

    -1

    8

     

     

     

     

     

     

     

     

     

     

     

    E

    5

    -4

    20

     

     

     

     

     

     

     

     

     

     

    F

    20

    -16

    20

     

     

     

     

     

     

     

     

     

     

    G

    40

    -15

    -5

    45

     

     

     

     

     

     

     

     

     

    H

    61

    -1

    -30

    45

     

     

     

     

     

     

     

     

     

    I

    41

    60

    -76

    41

    49

     

     

     

     

     

     

     

     

    J

    -100

    202

    -143

    37

    49

    0

     

     

     

     

     

     

     

     

     

     

    In the above example it can be seen that several well defined formatted columns could be generated from single column #A. larger the integers in col. #A. larger will be the generated # columns. If the last cell of col. #A is substituted with variable X. all the end cells of each subsequent columns will have different values with X+ or X- .

    Important : - in selecting any two columns in forecasting applications, the top two paired nos. in the columns should be lined in a row. 

     

    In conclusion, there are many such features that somebody can explore by using the computes and by selecting large populations. May be, some of the features thus found  are more interesting and more potent in the applications of many probability forecasts.

     

     

     

     

     

     

     

     

     

     

     

     

     

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      bgonçalves
      Brasil
      Member #92566
      June 9, 2010
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      Posted: January 21, 2013, 6:27 pm - IP Logged

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      Hello, ok laker, you can adapt to pick3, making pick3 each column, using the last six contests, then we can use the concept or even better, you can use a 49/6, analyzing the final digits from 0 to 9, like two pisck3., ie can adapt in various lotteries, the carlig, can help us, he can use the concept.

        Avatar
        New Member
        Quebec
        Canada
        Member #136083
        December 3, 2012
        4 Posts
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        Posted: January 21, 2013, 8:23 pm - IP Logged

        This is not a new sistem : http://www.lotterypost.com/thread/243708

          retxx's avatar - mrthumbs
          BOSTON
          United States
          Member #48
          September 9, 2001
          3092 Posts
          Offline
          Posted: January 21, 2013, 8:44 pm - IP Logged

          Hey Dr. San get ahold of carlig right away. Watch her simplify your program so we can digest it more easily. She is great at solving these programs. Bash

            JKING's avatar - Kaleidoscope 3.gif

            United States
            Member #5599
            July 13, 2004
            1149 Posts
            Offline
            Posted: January 22, 2013, 12:04 am - IP Logged

            Let us take events of a lottery of daily draw. Let the following numbers be the results of daily draw of a single digit lottery

            1, 5, 8, 3, 6, 7. ……… If you look at the numbers, you will find that the events are totally at random in occurrence and absolutely with no relevance in between them. You cannot predict the next lottery number however expert you may be in statistics. There is a total uncertainty in forecasting next number. The BEST method in forecasting the next event is ‘conditional probability method ‘. In this method, another parallel format of  event  for each occurrence of numbers is taken in account and future event is predicted against the occurrence of the number in the conditional format. This method is known as ‘linear regression method ‘ In simple terms predicting the future value by using existing values. The predicted value is a Y value for a given X value.  The known values are existing x-values and y-values, and the new value is predicted by using linear regression. You can use this function to predict future sales, inventory requirements, or consumer trends, in forecasting gambling, horse racing and many more. Given below are STEPS, which will make you to understand the NEW CONCEPT and how to use it in forecasting future events without much fuss and in utmost probability levels.

             

             

             

                                                                        STEP -1                                 

             

                                                                                                                                                           

            Select some random variable serial wise and lay those in a column K as below and in the left side column are alphabets denoting the corresponding integer on the right side. Let us select six random variables.

                                                                        STEP - 2

             

             

             

             

            Subtract the lower integer from the top integer of column K  and display the results in the next column as shown below. The procedure goes as 1 – 5 ( A – B ) = - 4,  5 – 8 ( B – C ) =  - 3,  ….. so on. Continue this procedure until you get single cell display at the end, as shown in figure 2.

             

             

             

             

             

             

                              Figure – 1                                                  Figure - 2

             

                # K

             

             

             

             

             

            A

            1

             

             

             

             

             

            B

            5

            -4

             

             

             

             

            C

            8

            -3

            -1

             

             

             

            D

            3

            5

            -8

            7

             

             

            E

            6

            -3

            8

            -16

            23

             

            F

            7

            -1

            -2

            10

            -26

            49

             

                K

             

            A

            1

             

              B

            5

            -4

            C

            8

            -3

            D

            3

            5

            E

            6

            -3

            F

            7

            -1

                                                           

             

             

             

              End nos.

              ( brown color)

             

                   

              End cell

             

                                                  ( End nos. or end cells are shown as brown with end cell)

                                                               

            In evolving further procedure, we will take the example of figure – 2 and displayed as below.                                                                                       

                                                                                                           

             

             

             

             

            this row contains  integers selected at random

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

              A

             

             

             

             

             

             

             

            # A

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

            A

            1

             

             

             

             

             

             

             

            1

            f

             

             

            B

            5

            -4

             

             

             

             

             

             

            1

             

             

             

            C

            8

            -3

            -1

             

             

             

             

             

            4

            -3

             

             

            D

            3

            5

            -8

            7

             

             

             

             

            7

            -3

             

             

            E

            6

            -3

            8

            -16

            23

             

             

             

            18

            -11

            8

             

            F

            7

            -1

            -2

            10

            -26

            49

             

             

            37

            -19

            8

            0

                                                                                                            Formatted triangle - above

             

             

             

                                                                  STEP – 3

             

             

             

             

            Add all the numbers of each row and display it in the column # A shown as above as

             

            In row A = 1 + 0 = 1, in row B =  5 + ( - 4 )  = 1,  in row C = 8 + ( - 3 ) + ( - 1 ) = 4………so on

             

            Continue this process till you gets a format on the left side and I call it as FORMATTED TRIANGLE and the first column as FORMATTED COLUMN or as # A  (brown in color)

             

             

             

             

                                                                  STEP - 4

             

             

             

             

            The formatted triangle, as mentioned above is the main fundamental feature of the formatting  and in the coming lines many interesting properties or you can say as interesting FEATURES are found in the FORMATTED TRIANGLE. Now we shall proceed further in evolving many interesting

             

             

             

             

            features that the formatted triangle contains. Let us first take the formatted triangle, shown as above

             

            Feature1). The top two digits, A & B will be same in value

             

             

             

             

            Feature no. 2). The difference of third integer from 2nd, and 4th  to 3rd will

             

              - be same. B – C = C – D, as seen in the next column as -3, -3

             

            1

             

             

             

            1     

             

             

             

            4

            -3

             

             

              7

            -3

             

             

            18

            -11

            8

             

            37

            -19

            8

            0

             

             

             

            Feature no. 3) the next integers, E & F will have the same difference when evolved further, seen as – 8, - 8.

             

            This is one fundamental property of formatted property and

             

             

             

            @ true to all formatted triangle formations for any given population of column of random nos.  A. shown in STEP-2

             

             

             

                                                                      STEP -5

             

             

             

             

            Here go the real action of explorations. The formatted triangle as worked out above is to be taken into account as many of interesting features could be found in evolving the formatted triangle further, as below.

             

             

             

             

            #  A

             

             

             

             

             

             

            A

            1

             

             

             

             

             

             

            B

            1

            0

             

             

             

             

             

            C

            4

            -3

            3

             

             

             

             

            D

            7

            -3

            0

            3

             

             

             

            E

            18

            -11

            8

            -8

            11

             

             

            F

            37

            -19

            8

            0

            -8

            19

             

             

             

             

             

             

             

            A

            1

             

             

             

            B

            1

            0

             

             

            C

            4

            -3

             

             

            D

            7

            -3

            0

             

            E

            18

            -11

            8

            0

            F

            37

            -19

            8

            0

             

             

             

                                                                                   

             

             

            Figure - 2

             

             

             

                                          Figure – 1                                               

                              (  Formatted triangle)

             

             

             

            Figure – 1 is formatted triangle as described above. When the digits displayed in the column # A is again further formatted, as shown in figure – 2, the same replica of  figure – 1 is seen . That is say that the totals of each row of triangle in figure – 1, will be same as of column # A. If you take the examples in STEP-2, the formatted triangle displayed in Figure -2  is not the replica of

            Figure - 1

            Feature no 4) The first column # A of formatted triangle is again formatted, it will be the same replica of the first triangle.

             

             

             

             

            Take the integers of column # A from figure – 1 as shown above and the end integers of same row. The display will be as below. Subtract the end nos. from column # A and observe the result.

             

             

             

             

             

            # A            end nos        #A – end nos.

            1 

             

            1

            1

             

            0

            4

             

            3

            7

             

            3

            18

             

            11

            37

             

            19

            0

            1

            1

            4

            7

            18

            The figures in this column is the result of #A – end nos.

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

              #A            RND                         

            1   

            1

            4

            7

            18

            37

            1

            5

            8

            3

            6

            7

                                                                                                                 

              Subtract column RND from column #A and the result will be as                             

            Displayed as below and

              Feature no 6) There is a conditional correlation between the original   Random nos. and its’ formatted sequences

              as seen in the extreme right column  wherein the differences

            between  the consecutive cells are displayed.                                                     

                                                               

            0

             

            -4

             

            -4

            0

            4

            0

            12

            -8

            30

            -18

             

             

             

             

             For next feature , let us take  the formatted olumn #A  and include ‘ 0 ‘ on the top cell as shown below  and repeat the formatting as explained in STEP -2, figure – 2.

             

             

                    #A        Zero start format

             

            0

             

             

             

             

             

             

             

              1

            -1

             

             

             

             

             

            1

            0

            -1

             

             

             

             

            4

            -3

            3

            -4

             

             

             

            7

            -3

            0

            3

            -7

             

             

            18

            -11

            8

            -8

            11

            -18

             

            37

            -19

            8

            0

            -8

            19

            -37

             

             

             

             

             

             

             

             

             

             

             

            0

             

             

             

             0

             0

             0

             0

             0

            0

            0

             

            Feature no 7) The totals of all the consecutive rows will always be equal to ‘ 0 ‘ as

            seen in the right side column. Feature no 8) The first cell and the consecutive

              cells running in diagonal format in the next row will always = 0.

             

             

             

             

             It can be seen from the above example that how the feature of display of ‘ 0 ‘  will be continuing diagonally in all the cells falling diagonally in the next consecutive rows and can be extended further to any length and displaying the totals of row integers as = 0 up to the last row.

            Feature no 9) Below each cell, staring with the first cell with ‘ 0 ‘ display and its’ diagonal cells with ‘ 0 ‘ displays in the consecutive rows will always have formatted conditional sequences. Let us observe the first column. You will find with ‘ 0 ‘ on top cell  and sequence below cells are conditional formats repeated in the next columns below each cell with ‘ 0 ‘ falling in the diagonal path for any extension.

            Feature no 10) The end nos. of each row will always have same value in negative as of the first nos. of the same row as seen in the above example, the last integer and the first integer of a row, are same but opposite and their totals will always = 0

                                                                                    STEP – 6

             

            In this section we will elaborate some more interesting features.

            For next feature, let us take the original random variable example as shown in STEP – 2, as displayed below

                       A                                                                                   A         end nos.               

            1

             

             

             

             

             

              5

            -4

             

             

             

             

            8

            -3

            -1

             

             

             

            3

            5

            -8

            7

             

                 

            6

            -3

            8

            -16

            23

             

            7

            -1

            -2

            10

            -26

            49

                        1              1                      2
                         5             -4                     1 
                          8            -1                     7
                          3              7                   10
                          6             23                  29
                          7             49                 56
             In the above example, the column is the display of original random variables selected and the subsequent columns are the display of column A, the end nos. and last one is the total of col. A and the end nos. of each row. Let us take the column of the ‘total’ for further evolution and exploring new features as below.

            Now we will triangle format the total column as explained in STEP – 2

            total

            2

             

             

             

             

             

            1

            1

             

             

             

             

            7

            -6

            7

             

             

             

            10

            -3

            -3

            10

             

             

            29

            -19

            16

            -19

            29

             

            56

            -27

            8

            8

            -27

            56

            Feature no 11) The differences between the integers and the subsequent end nos. of

             

              each row will be of same value. In this example the

              difference found is = 0( not necessarily =0 and can be of any value)

             

             

             

             

             

             

             

             

             

            In continuation for some more features, let us take the original random variables as shown in STEP – 2. Take the end nos. ( in boxes) of each row of  format – 1, and display them in  the first column of format – 2, as below

             

                            Format - 1                                                            format - 2

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

            1

             

             

             

             

             

             

             

            1

             

             

             

             

             

             

            5

            -4

             

             

             

             

             

            -4

            5

             

             

             

             

             

            8

            -3

            -1

             

             

             

             

            -1

            -3

            8

             

             

             

             

            3

            5

            -8

            7

             

             

             

             

            7

            -8

            5

            3

             

             

             

            6

            -3

            8

            -16

            23

             

             

             

            23

            -16

            8

            -3

            6

             

             

            7

            -1

            -2

            10

            -26

            49

             

             

            49

            -26

            10

            -2

            -1

            7

             

             

             

             

             

             Feature no 12) The integers of first column of format – 1 are formed as end nos. of format -2 and the integers of end nos. of format -1 are formed in the first column of format -2 and vice versa.

             

                                                                          STEP – 7

             

             

             

             

            Till now we have taken only six random variables for triangle formatting. We shall go further in selecting more random variables for exploring some more features and verifications. Let us take ten random variables in series triangle format it as described in  STEP – 2.

             

             

             

            A

             

             

             

             

             

             

             

             

             

             

            5

             

             

             

             

             

             

             

             

             

            5

            7

            -2

             

             

             

             

             

             

             

             

            5

            4

            3

            -5

             

             

             

             

             

             

             

            2

            0

            4

            -1

            -4

             

             

             

             

             

             

            -1

            5

            -5

            9

            -10

            6

             

             

             

             

             

            5

            7

            -2

            -3

            12

            -22

            28

             

             

             

             

            20

            2

            5

            -7

            4

            8

            -30

            58

             

             

             

            40

            7

            -5

            10

            -17

            21

            -13

            -17

            75

             

             

            61

            1

            6

            -11

            21

            -38

            59

            -72

            55

            20

             

            41

            6

            -5

            11

            -22

            43

            -81

            140

            -212

            267

            -247

            -100

             

            Take the formatted column #A and display it as below denoting each cell with alphabetic letters on the left side.

             

             

                                                          VIEW - 2

             

            A

            B

            C

            D

            E

            F

            G

            H

            I

            J

              #A

            5

            5

            2

            -1

            5

            20

            40

            61

            41

            -100

             

             

             

             

             

             

             

              =

            A

             

             

             

             

             

              =

            A

             

             

             

             

             

              =

            A -B +C

             

             

             

             

              =

            A-2B+2C

             

             

             

             

              =

            A-3B+4C-2D+E

             

             

             

              =

            A-4B+7C-6D+3E

             

             

             

              =

            A-5B+11C-13D+9E-3F+G

             

             

              =

            A-6B  +16C-24D+22E-12F+4G

             

              =

            A-7B+22C-40D+46E-34F+16G-4H+I

              =

            A-8B+29C-62D+86E-80F+50G-20H+5I

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

            Feature no. 12). The formation of column #A can be calculated by formulas as described on the right side format without doing for real time triangle formatting as of VIEW - 1

              Feature no) 13). Periodicity of alphabetical order is seen in the order of formulas.

            If you look at the formulas,  VIEW – 2, the periodicity of display order is seen as column wise as A, A, A, A, …….B, 2B, 3B, 4C, ……..C, 2C, 4C, 7C, 11C, ….and so on

             

             

             

            The formatted column #A, some more fundamental properties numbering 14, 15, 16, & 17) and the formulas may be of much helpful in many statistical applications.

             

             

             

             

             

             

             

             

             

             

             

            Examples

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

              14)

            B-2C+D  = 0

             

             

             

            5 - 2*2 +  ( -1 ) = 0

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

              15)

            C-3D+3E-F  = 0

             

             

            2 - ( -1  )*3 + 5*3 - 20 = 0

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

              16)

            D-4E +  6F - 4G + H = 0

             

            ( -1 ) -   (5 )*4 + 20*6 - 40*4 + 61 = 0

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

             

              17)

            E - 5F  +10G - 10H + 5I - J = 0

            5 -   (20)*5 + 40*10 - 61*10 + 41*5 - 100 = 0

             

             

             

            Feature no18) Periodicity of alphabetical order is also seen in the display of above formulasas described in feature no 13). In evolving further such features in bigger populations, computer application is needed to identify such equations as described above and also it is a matter of working this new concept on the computer surely many of similar more features could be found with the help of the computer in working with large population of data. 

             

                                                                      STEP – 8

             

             

             Before going further, it is important to understand the above concepts and the said features by working with different small samples on paper, preferably on Microsoft Excel work sheet on computer and test the features.

             

            USE OF THE NEW CONCEPT IN PROBABILITY, FORECAST 

             

            How this concept can be incorporated in evaluating probability & forecast, particularly when the population contains random and uncertainty level ? let us take some examples and work out implementing some of the said features. Sample 1s taken from STEP -7, WIEW – 1.

                             

             

            A

             

             

             

             

             

             

             

             

             

              #A

            A

            5

             

             

             

             

             

             

             

             

             

            5

            B

            7

            -2

             

             

             

             

             

             

             

             

            5

            C

            4

            3

            -5

             

             

             

             

             

             

             

            2

            D

            0

            4

            -1

            -4

             

             

             

             

             

             

            -1

            E

            5

            -5

            9

            -10

            6

             

             

             

             

             

            5

            F

            7

            -2

            -3

            12

            -22

            28

             

             

             

             

            20

            G

            2

            5

            -7

            4

            8

            -30

            58

             

             

             

            40

            H

            7

            -5

            10

            -17

            21

            -13

            -17

            75

             

             

            61

            I

            1

            6

            -11

            21

            -38

            59

            -72

            55

            20

             

            41

            J

            6

            -5

            11

            -22

            43

            -81

            140

            -212

            267

            -247

            -100

                       

                              The numbers displayed in the column A is selected randomly and triangle formatted as described in STEP – 2. 

            The numbers displayed in #A column are formatted by adding integers on the left format row wise. As said that the two columns A  &  #A will have conditional probability, we will take the two columns separately and work out.