[Tutor] What's the best way to model an unfair coin?

Steven D'Aprano steve at pearwood.info
Sun Oct 24 18:22:40 CEST 2010

Richard D. Moores wrote:

> Actually, I used the unfair coin model as the simplest example of the
> kind of thing I want to do -- which is to model the USD->Yen exchange
> rate. I want the next quote to vary in a controlled random way, by
> assigning probabilities to various possible changes in the rate. See
> <http://tutoree7.pastebin.com/mm7q47cR>. So I assign probability 1/40
> to a change of plus or minus .05; 3/40 to .04; 5/40 to .03, etc.

Another approach you might take is to model the change as a normal 
distribution (bell curve probability) rather than uniform. This is 
probably more realistic. It would make most sense to have it symmetrical 
around zero, so you want a random number with a normal distribution, a 
mean of zero, and a standard deviation yet to be determined.

To determine the standard deviation, use this rule of thumb: for a 
normal (bell) curve, approximately 68% of events are plus or minus one 
standard deviation from the mean; 95% are plus or minus two std 
deviations; and 99.7% are plus or minus three std deviations.

So if you decide that 99.7% of the time the change in exchange rate 
should be less than 1.00, for example, that corresponds to a std 
deviation of 0.333.

You then generate a normally-distributed value using the random module, 
round it to two decimal places to correspond to cents, and Bob's your uncle.


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