Problem 1. Let a, b, c be real numbers such that a b 0. If (X,...

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Problem 1. Let a, b, c be real numbers such that a b 0. If (X, Y) has a joint p.d.f. f(x,y), what's the joint p.d.f. U := a X+c Y and V := b Y? . Problem 2. (Continuation.) Specialize your findings in Problem 1 when X and Y are independent, each Normally distributed with mean 0 and variance 1, and a = b = 1 and c = 1. Problem 1. Let a, b, c be real numbers such that a b 0. If (X, Y) has a joint p.d.f. f(x,y), what's the joint p.d.f. U := a X+c Y and V := b Y? . Problem 2. (Continuation.) Specialize your findings in Problem 1 when X and Y are independent, each Normally distributed with mean 0 and variance 1, and a = b = 1 and c = 1.