In the previous example, the color of the Quantum Points is a Gray Gradient from Light to Dark. The Darker the Quantum Point the more Probable you would likely find an actual data point. This is ok, but it doesn't clearly define what more probable than other areas of the graph. This is where a Color Gradient comes in. It helps with showing the more probable areas without taking away from the whole Quantum Point Graph. The following picture show how to read the graph's Color Gradient.

The scale is called Probability Density because the higher the value the more densely packed the data is in those areas. Next is the previous graph in a Color Gradient format.

From this it's even more obvious where the data is tending to be and how the data ebbs and flows as more data is collected.

post continues...

Can you explain a little more?

Are the pictures not showing or is it something else?

Those symbols in those equations.

ah, got ya. i'll try to keep it as simple as possible. however, i do like to give out the information for those that would like it. don't worry about the math stuff, just look over the whole thing to get a feel for what is being talked about. i'll present it in both ways if possible, so everyone can be in on it.

Interesting graph --so how exactly are the equations related to the graph. are you trying to relate that greater the probablity density then choose in that area?

How do the equations differ from normal distribution?

there's log normal distribution ect.

There are many forms of distribution.Please define your terms.

I'd still perfer  pdfs of your posts containing explainations.

In what book or books --are you using for reference material?

Thank - you

I haven't forgot about ya. I'm working out a display format for both the PDF's at my webspace and here at the Lottery Post.

The following work is still in progress.

I'm just releasing what I have now and will update more later.

You can also see the following posting in a PDF format at my website http://home.mchsi.com/~jadelottery.

The post has to be in an image format here at the Lottery Post because of the displayed math equations.

To see the equations better, visit my website for the PDF's.

You will need Adobe Reader or Adobe Acrobat to view the PDF's and you can get it at http://www.adobe.com.

The Reader is a free download.

Firstly, thank you for the PDF. AS moving graphics don't print well. Solid things that can be printed I can view off line.

Great !

Some things I'm trying to answer:

Many digital electronic book authors, have stated that the Normal distribution function equation can be used to derive uniform random numbers--like a rng does.

One author: Steven W. Smith --Digital Signal Processing Isbn 0-750674-44-x

He states that if the mean of the equation is .5 and the SD is the sqr(12)^-1 then x is supposed to uniform via Iterative recursion.

Jade, would you please explain how quantum distribution is/could be involved to derive random variates?

Thanks again...

I'll get back to this probably next week.

I will be traveling to Wisconsin and possibly Illinois this weekend; in addition to finishing the Quantum Points PDF.

you fail to answer the question of why any state would FIX the drawing of the numbers.  They take there cut of the money BEFORE the pay out on the big games. The odds of paying out on the daily 3 and 4 games is in there advantage. The have a money maker. Why would they do any thing to casue public mistrust????????   Most states are very happy making 300 to 400 million a year.