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Let Y be a nonnegative random variable. Prove that E(Y) = 0 if and only if P(Y = 0) =1. (You may…

Let Y be a nonnegative random variable. Prove that E(Y) = 0 if and only if P(Y = 0) =1. (You may assume for simplicity that Y is discrete, but the result is true for any Y.)