54. Let X and Y each take on either the value 1 or 1. Let p(1, 1)...

54. Let X and Y each take on either the value 1 or −1. Let

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p(1, 1) = P(X = 1, Y = 1}, p(1, 1) = P(X = 1, Y=-1), p(-1, 1) = P(X=-1, Y = 1}, p(-1,-1) = P(X = -1, Y=-1} Suppose that E[X]=E[Y]=0. Show that (a) p(1, 1)p(-1, -1); (b) p(1, -1)p(-1, 1). Let p 2p(1, 1). Find (c) Var(X); (d) Var(Y); (e) Cov(X, Y).