Exercise 2: Suppose that the joint pdf of (X,Y) is fx.x(r, y) = c(r + y), if r E 0, 1,2, 3 and y € 0, 1, 2,3. a: What is the value of c? b: What are the marginal pdfs fx(r) and fy(y)? c: What is E(Y...

Extracted text: Exercise 2: Suppose that the joint pdf of (X,Y) is fx.x(r, y) = c(r + y), if r E 0, 1,2, 3 and y € 0, 1, 2,3. a: What is the value of c? b: What are the marginal pdfs fx(r) and fy(y)? c: What is E(Y |X = 3) ? d: What is cov(3X – 5, Y)? Hint: Covariance is linear in each coordinate. That means two things. First, you can pass constants through either coordinate: Cov(aX, Y) = a Cov(X,Y) = Cov(X, aY) Second, it preserves sums in each coordinate: Cov (X1 + X2, Y) = Cov (X1, Y) + Cov (X2, Y) For example: if X2 = c, so X2 is a constant, then Cov (X1 + X2, Y) = Cov (X1, Y) + Cov (c, Y) = Cov (X1, Y)