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Math Help - Bell Curves

  1. #1
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    Bell Curves

    can somebody show me proof that a binomial distribution and a hypergeometric distribution both approach normal distributions
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by JeffN12345 View Post
    can somebody show me proof that a binomial distribution and a hypergeometric distribution both approach normal distributions
    For the binomial it is just the central limit theorem.

    The number of successes in N trials is the sum of N iid RV taking the value 1 with probability p and 0 with probability (1-p). These have mean p and variance p(1-p). Hence the distribution of the sum tends to normality with mean Np and variance Np(1-p).

    (the hypergeometric case is dealt with by first using the binomial approximation when appropriate that by the normal)

    CB
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