Question: Problem 3.31 Let X be a Bernoulli random variable. Show that V (X) 1 4 . Hint: The variance of a Bernoulli random variable

Problem 3.31 Let X be a Bernoulli random variable. Show that V (X) ≤ 1 4 . Hint: The variance of a Bernoulli random variable is given by V (X) = p(1 − p) (see Equation 3.22). Then show that p(1 − p) ≤ 1/4.

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