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If X∼Binom(n,p), E[X] = np. Calculate V[X] = np(1−p) by: a) First show E[X(X−1)] + E[X]...

If X∼Binom(n,p), E[X] = np. Calculate V[X] = np(1−p) by:

a) First show E[X(X−1)] + E[X] − (E[X])^2 = V[X] (Hint: Use propertie of E[·] and V[·]).

b) Show E[X(X−1)] = n(n−1)p^2

c) Use E[X] = np, a) and b) to discuss, V[X] = np(1−p).

Math   Statistics-And-Probability   
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Answer #1

a)

Now,

b)

c) Variance of X =

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