4.55.* From the formula on page 72, the standard deviation of a discrete probability distribution is

(a) When y can equal only 0 and 1, letting π = P(y = 1)
and 1 − π = P(y = 0), show that μ = π and that σ =
π(1 − π).

(b) Show that the standard error of a sample proportion for a random sample of size n equals
π(1 − π).

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