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Normal distribution simulation

I have two requirements. The first involves estimating "win" probabilities for a given set of variables. As the variables are assumed to be drawn from a normal distribution, I imagine this will be done by running a random number simulation based on a normal distribution for a given number of trials and counting the number of times each variable had the lowest value in any one trial. If anyone has a better (quicker and or more accurate) way of doing this e.g. Markov Chain Monte Carlo that would also be fine.

The second is essentially the opposite of the first but would need I believe an iterative approach. Essentially I want to be able to feed in x variables representing probabilities (summing of course to 1). Each probability variable would also have its associated standard deviation. The system would trial different means for each variable until it has a mean for each variable that when run through the simulation program developed above would approximately (+/- 2%?) match the input probabilities. Again a normal distribution would be assumed.

I have attached a spreadsheet example of what I want for the first problem. I have used the excel random number generator using the normal distribution to arrive at the simulation and estimates. I will use this process to test the code so please indicate if you expect the program to generate significantly different results to an excel simulation on the same inputs.

## Deliverables

1) Complete and fully-functional working program(s) in executable form as well as complete source code of all work done. Also example VB Script code for implementing program via VB Scripting interface.

2) Deliverables must be in ready-to-run condition, as follows (depending on the nature of the deliverables):

a) For web sites or other server-side deliverables intended to only ever exist in one place in the Buyer's environment--Deliverables must be installed by the Seller in ready-to-run condition in the Buyer's environment.

b) For all others including desktop software or software the buyer intends to distribute: A software installation package that will install the software in ready-to-run condition on the platform(s) specified in this bid request.

3) All deliverables will be considered "work made for hire" under U.S. Copyright law. Buyer will receive exclusive and complete copyrights to all work purchased. (No GPL, GNU, 3rd party components, etc. unless all copyright ramifications are explained AND AGREED TO by the buyer on the site per the coder's Seller Legal Agreement).

## Platform

Windows XP

スキル: PHP

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