Question: Suppose that X Binomial(n, p): i.e., that X is the sum of the number of successes observed in n independent trials, each of which has

Suppose that X Binomial(n, p): i.e., that X is the sum of the number of successes observed in n independent trials, each of which has success probability p. One can show that the characteristic function of X is then X(t) = (1 p + pe^it)ⁿ . Using this fact, verify that E[X] = np and Var(X) = np(1 p).

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