Question: (a) Show that (f(x1)f(X2))(g(x1)- 8(X2)) is a non-negative random variable. (b) Now suppose that X1 andX2 are independent and equi-distributed. Show that 2Cov(f(x1), 8(X1))

(a) Show that (f(x1)f(X2))(g(x1)- 8(X2)) is a non-negative random variable. (b) Now suppose that X1 andX2 are independent and equi-distributed. Show that 2Cov(f(x1), 8(X1))

(a) Show that (f(x1)f(X2))(g(x1)- 8(X2)) is a non-negative random variable. (b) Now suppose that X1 andX2 are independent and equi-distributed. Show that 2Cov(f(x1), 8(X1)) - = Cov(f(x1)- f(x2),g(X1) g(X2)). (c) Show that Cov(f(x1), 8(X1)) 0. 3) Suppose and g are non-negative bounded Borel functions. Let X and X2 be random variables

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