Problem 2 Let the two random variables X and Y be independent, with the following Cumulative Distribution Functions (CDFS): x < -2 x<-2 1 (x+2) -2 0 Fx(x) = Fy(y) = 1 1 x >0 We want to: a) Compute and draw the two corresponding pdfs; b) Compute E[X], E[Y), var(X), var(Y); c) Compute the mean and variance of the r.v. Z = X+Y; d) Let V = 4X + 2; compute and draw the pdf of V; compute E[V] and var(V)

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