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Thread: Standard deviation of a set of random odds

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    Standard deviation of a set of random probabilities




    Imagine I have n mutually exclusive events whose probabilities are perfectly random. The sum of their probabilities is 1 of course. What is their most likely standard deviation, if there is one?

    Playing around with R, it looks like there is one. If n is 10, for example, the standard deviation tends to 0.05891 .

    Code: 
    > gen <- function (n) { x <- runif(n, 0, 1); x <- x / sum(x); x; }
    > mean(replicate(10000000, sd(gen(10))))
    [1] 0.05891704
    What I would like to understand is:

    a) Is what I found a known property of random distributions of probability? Or it is an aberration caused by using software random number generators?

    b) If the answer to (a) is yes, how is this phenomenon called, so that I can find out more? And in particular...

    c) Is there an exact formula to calculate the ideal sd value as a function of the number of events?

    Thanks,

    Giacecco
    Last edited by giacecco; 01-07-2014 at 01:28 PM. Reason: Clarified what I would like the community to tell me

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    Re: Standard deviation of a set of random odds

    Note that there is a difference between 'odds' and 'probability'. I think you're looking at probability.
    I don't have emotions and sometimes that makes me very sad.

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    Re: Standard deviation of a set of random probabilities


    And I guess I'm wonder what you're looking for somebody to explain?
    I don't have emotions and sometimes that makes me very sad.

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