please help with the following questions

5.108. Let h(x, y) be a joint Gaussian pdf for zero-mean, unit-variance Gaussian random vari- ables with correlation coefficient p . Let g(x, y) be a joint Gaussian pdf for zero-mean. unit-variance Gaussian random variables with correlation coefficient pz # p. Suppose the random variables X and Y have joint pdf fxy(x. y) = {h(x, y) + g(x. y) }/2. (a) Find the marginal pdf for X and for Y. (b) Explain why X and Y are not jointly Gaussian random variables.The joint Gaussian probability density function of random variables X and Y is given by 1 fx, x (x, y) = - exp -x2 - xy - 1.5y"] . 2 TT Two new random variables W and Z are obtained by the transformation =. la. Find the covariance matrix Cxy of the joint Gaussian random vector [X Y]T. 1b. Find the covariance matrix Cwz of the joint Gaussian random vector [W Z ]T. 1c. Find the joint probability density function fw,z(w, z) of the random variables W and Z.Exercise 1. Jointly Gaussian random variables. Let X and Y be jointly Gaussian random variables with pdf fx, y (x, y) = e- z(3x2+16 y2. y'+ ;xy-8x-16y+16) 7 3/4 Find E(X ), E(Y), Var(X), Var(Y ), Cov(X, Y).Jointly Gaussian Random Vanable Let Y = denote a Gaussian random vector with mean My [0, b] T and covariance Ey (44 for some b E fR . Verity J. is a valid covariance matrix