Suppose X and Y are jointly Gaussian such that X is N (0, 16), Y is N (0, 9), and the correlation coefficient is denoted by p. For two jointly distributed Gaussian random variables, they are independent if and only if they are uncorrelated. The solution to the questions below may depend on p and may fail to exist for some values of p. (a) For what value(s) of a is X independent of X + aY? (b) For what value(s) of d is 2X + dY independent of (X dY)2? If d exists, providing one value of d is sufcient