• Let X and Y are two independent random vari- ables. If E(X) = 0 and E(Y) = 0. Prove that Var(XY) Var(X) Var(Y). A player tosses 3 coins. He wins * 16, if 3 heads appear, 8 if 2 heads appear, ? 4 if...

Extracted text: • Let X and Y are two independent random vari- ables. If E(X) = 0 and E(Y) = 0. Prove that Var(XY) Var(X) Var(Y). A player tosses 3 coins. He wins * 16, if 3 heads appear, 8 if 2 heads appear, ? 4 if 1 head appears and ? 2 if no head appears. Find his expected amount of winning.