Question: =+16. If the random variable X has values in the interval [a, b], then show that Var(X) (b a)2/4 and that this bound

=+16. If the random variable X has values in the interval [a, b], then show that Var(X) ≤ (b − a)2/4 and that this bound is sharp. (Hints: Reduce to the case [a, b] = [0, 1]. If E(X) = p, then demonstrate that Var(X) ≤ p(1 − p).)

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