Let f(x, y) = (2/ 2 )e (x+y) / , 0 < x < y < ,

Let f(x, y) = (2/θ²)e^−(x+y)/θ, 0 < x < y < ∞, zero elsewhere, be the joint pdf of the random variables X and Y .
(a) Show that the mean and the variance of Y are, respectively, 3θ/2 and 5θ²/4.
(b) Show that E(Y |x) = x+θ. In accordance with the theory, the expected value of X + θ is that of Y , namely, 3θ/2, and the variance of X + θ is less than that of Y . Show that the variance of X + θ is in fact θ²/4.