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Math Help - Binomial random variable

  1. #1
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    Binomial random variable

    Let X be a Binomial random variable with parameters n; . Prove the
    expectation and variance of X are n(pi) and n(1-pi) respectively. (Hint: use
    the defi…nition of expectation and variance and the relation between Bernoulli
    and Binomial.

    So E(x) = sum(xP(x)) and Var(x) = sum((x-u)^2*P(x))

    Not really sure where to go from here. P(x) for binomial is equal to n!/x!(n-x)!*pi^x*(1-pi)^(n-x)
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  2. #2
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    Remember that a binomial R.V. is simply the sum of n independent Bernoulli trials. Also recall that:
    E(\sum X)=\sum E(X)
    This should help you figure out those expectations.
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