46. If X and Y have the joint probability distribution
f(-1,0) = 0, f(-1,1) = \frac{1}{4}, f(0,0) = \frac{1}{6}, f(0,1) = 0, f(1,0) = \frac{1}{12}, and f(1,1) = \frac{1}{2}, show that
(a) cov(X, Y) = 0;
(b) the two random variables are not independent.
49. If X1, X2, and X3 are independent and have the means
4, 9, and 3 and the variances 3, 7, and 5, find the mean and
the variance of
(a) Y = 2X1 - 3X2 + 4X3;
(b) Z = X1 + 2X2 - X3.