Let Y, X be independent and square-integrable random variables, and let Z = max(Y + X, 0) Show that if 1. E(X) < 0 and Y and Z are iid, then Var(X) 2 |E(X)| E(Y) = E(Z) < 2. E(X) > 0 and E(Y) > 0, then E(Z) > E(Y)+ E(X)

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