Suppose that x and yare continuous random variables with

Question

Question: 1. Suppose that X and Yare continuous random variables with the joint probability density function

(a) Find k, E(X), E(Y), V(X), V(Y), and cov(X, Y). Are X and Y independent?

(b) Find the marginal densities of X and y.

(c) Find the conditional density of X given Y = ½ and hence E(X|Y = ½) and V( Y|X = ½).

2. Given that y = e^x is normal with mean 2 and variance 4, find the mean and variance of x.