Problem 1: 50% Let Y = X+0X2 and Y = X + X for some constant a. Suppose that Y and Y2 are uncorrelated, each with zero mean and unit variance. a) Find the mean vector #, and the covariance matrix R, of col{X1, X2). b) Find the correlation coefficient pz for {X1, X2). c) If, in addition to the above assumptions, (Yi, Y2} are jointly Gaussian. What is the pdf of col{ X1, X2}? d) Continuing Part c), for which value of a X1 and X2 are statistically independent identically distributed? Find the pdf of col{ X1, X2}.