Let X and Y be jointly Gaussian random variables with mean E X] = /x and E[Y] = MY, variance var(X) = ox and var(Y) = of, and correlation coefficient p. (a) Using the notation given above, express the joint PDF of X and Y. Hint. Remember the PDF of jointly Gaussian random variables we have learned in class. (b) Now we define two new random variables W = X +Y and V = X -Y. Under what conditions is W and V independent? You can write the condition in terms of the notation above. Hint. Two jointly Gaussian random variables are independent if they are uncorrelated