EECS 55 - Engineering Probability Homework #8 Due: Mar 14, in class 1) If X~N(3, 4), Y~N(-2, 6), Z~N(1, 3), and X and Y and Z are independent, what are the distribution, expectation and variance of S = 3X-2Y+Z? Notation: N(3, 4) is a Normal RV with mean 3 and variance 4. 2) If X is uniformly distributed over (0,1) and Y is exponentially distributed with parameter = 1 and X and are independent, find the pdf of Z = X+Y. 3) The joint density function of X and Y is given by f(x,y) = xe-x(y+1) x>0, y >0 a. By just looking at f(x,y), say if X and Y are independent or not. Explain. b. Find the conditional density of X, given Y=y. In other words, fx|y(x|y). c. Find the conditional density of Y, given X=x. 4) The joint density function of X and Y is a. Compute the joint density function of U = XY, V=X/Y. b. What are the marginal densities of U and V? 5) Let X and Y be random variables with 2e x e y 0 y x fX,Y(x,y) = o.w. 0 Find E[XY], Cov(X,Y), and X,Y