3. Jointly Gaussian normal distribution is very important in probability theory and is used in many different applications such as signal detection and estimation, Bayesian inference, etc. In the problem, we derive some important properties of jointly Gaussian random variables. Consider the jointly Gaussian random variables X and Y that have the following joint PDF: 1 f x x (x, y) = 2pary exp -+ 2ToxoY V 1 - p2 2(1 - p2) X OXOY (a) Prove that Y is a Gaussian random variable by deriving its marginal PDF, fy(y). Find the mean and variance of Y. (b) Prove that fxy(x y) corresponds to another Gaussian random variable, then find its mean and variance