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2 Various Variance Problems (a) Suppose that X and Y are both binomial random variables with parameters n and p. If Var(X Y) = 2,

2 Various Variance Problems

(a) Suppose that X and Y are both binomial random variables with parameters n and p. If Var(X Y) = 2, what is cov(X,Y)?

(b) Prove that if X and Y are independent random variables, then Var(XY) = Var(X)Var(Y) +E[X]²Var(Y) +E[Y]²Var(X)

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