Be thorough and clear. PLEASE DONT SAY DENSITY OF Z IS NORMAL WITH MEAN AND VARIANCE. FIND THE CORRECT DENSITY.

Suppose that X and Y are jointly Gaussian with mean 1 and 3 respectively and vari- ances 2 and 2 respectively. That is, X N N (1, 2) and Y N N (3,2). In addition, suppose the the covariance between X and Y is 1. Suppose that Z = X + 21'. (a) Determine the mean of Z. (b) Determine the variance of Z. (c) Determine the density of Z. (d) Determine the probability that Z > 1. Express you answer in terms of the Q function or (I) function