Exercise 1 (Random vectors) (-) Let X] and X2 be independent and identically distributed (i.i.d.) as exponential with rate parameter A = 1. Find the joint pdf of Y, and Y2, where Y, = X, + X, and Y2 = Xi/(X1 + X2). Exercise 2 (Gaussian random vector) (-) Consider a random vector X ~ N(0, I,), where In E Rx^ is the unit matrix, and an orthonormal matrix U c R*x2. Prove that there holds UX ~ N(0, I,) without relying on the definition of the density of a Gaussian random vector