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Math Help - Binomial trials problem

  1. #1
    Junior Member
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    Binomial trials variance

    Hi all,

    I am beginning to look at some probability problems, I am completely new to college level probability, so not sure if this is in the right sub forum (maybe it should be in the basic?- guess mods will decide.)

    Given a scenario where there is a true statistic - proportion voting yes in a vote denoted by p , we sample n people from the large population

    For a binomial distribution for the sample where x denotes the number of yes votes:

    b(x;n,p) = \binom {n}{x} p^{x} (1-p)^{n-x}

    mean(b_i) = np ; var(b_i) = np(1-p) since the binomial distribution is a 'sample' of the true statistic, we need to take into account the standard error:

    var(bi) = {\sigma(p)^2 \over \sqrt{n}}n = \sigma(p)^2 \sqrt{n}

    I have multiplied by n to scale the variance up from the true average.... is this correct?

    Does that mean the z stat for the normal distribution approx becomes:

    z = {X- np \over \sqrt{\sigma(p)^2 \sqrt{n}}}

    Many thanks for reading! Any pointers wil be much appreciated.
    Last edited by padawan; September 6th 2010 at 01:34 PM.
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  2. #2
    Junior Member
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    I have simplifed the problem down to what I am contemplating... apoligies for the long winded garbled original post.
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