1. If the joint probability density of X and Y is given by
f(x,y) = (x+y)/3 for 0<x<1, 0<y<2 and 0 elsewhere.
- Find the variance of W=3(X) +4(Y) - 5.
2.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=2(X1) - 3(X2) + 4(X3);
(b) Z=(X1) + 2(X2) - (X3);
(c) find cov(Y,Z).