Problem 4 Matlab Experiment: Correlated Gaussian Random Variables (a) Generate 5000 2 x 1 Gaussian vectors X, with zero mean and identity covariance matrix (X=randn (5000, 2) ; ). Plot the samples as points on an (@, y) plane. You should see that the points indicate a circular pdf. (b) We wish to transform X to the Gaussian random vector Y = AX + b such that YNN ([2 ] . [3 :1) Find the vector b and matrix A to do so.(c) Generate 5000 samples of Y by transforming the samples of X using your values of A and b, and plot the points on the (r, y) plane as before. Do the plots match your intuition? (d) Find the pdf of the first and second coordinates of Y' (call them Y, and Y2). Plot the histograms of Y1 and Y2, and overlay on them plots of their corresponding true pdfs