Suppose that (X, Y ) can be described by the joint CDF:

FX,Y (x, y) = 1 - - +

Show That

FX,Y (x, y) = [(1 + x)(1 + y) − ] , x, y > 0, [0, 1].

Suppose that = 0. Explain why X and Y are independent?

Show that fX(x) = e−x, x > 0. (use = 1 + x

Calculate fY|X(y|x) and use it to compute E[Y|X = x]

N.B (where i have used the word "theta", obviously i have meant to use the symbol, but i was having problems doing latex math inside of latex math so used the word, so on each occasion where it is used, it should read " xy" hope it doesnt cause confusion)