6.1 (Video 4.1 - 4.7, Lecture Problem) Let X be Uniform[1,2]. Let Y given X = x be Exponential(x); that is, fY |X(y|x) = xexy,y 0 and 0,y < 0. (a) Find the expected value of Y . (Hint: see HW 5, problem 5.4e). (It is OK to leave your answer as an integral.) (b) Find the conditional expected value E[Y |X = x] of Y given X = x. (This should be in closed form.) (c) Using E[Y ] = E[E[Y |X]] find the expected value of Y . (This should be in closed form.) (d) Solve for E[XY ]