For k random variables X1, X2, . . . , Xk, the values of their joint moment- generating function are given by E(et1X1+ t2X2+ · · · + tkXk)
(a) Show for either the discrete case or the continuous case that the partial derivative of the joint moment-generating function with respect to ti at t1 = t2 = €¦ = tk = 0 is E( Xi).
(b) Show for either the discrete case or the continuous case that the second partial derivative of the joint moment- generating function with respect to ti and tj, i ‰  j, at t1 = t2 = €¦ = tk = 0 is E(XiXj).
(c) If two random variables have the joint density given by

Find their joint moment- generating function and use it to determine the values of E(XY), E(X), E(Y), and cov(X, Y).

Transcribed Image Text:

e-k-y for x>0, y 0 0 elsewhere f(x,y) =