13. Let X ~ N(0, 1) and let Y = eX. (a) Find the pdf for Y . Plot it. (b) (Computer Experiment.)…

13. Let X ~ N(0, 1) and let Y = eX. (a) Find the pdf for Y . Plot it. (b) (Computer Experiment.) Generate a vector x = (x1,…,x10,000) consisting of 10,000 random standard Normals. Let y = (y1,…,y10,000) where yi = exi . Draw a histogram of y and compare it to the pdf you found in part (a). 14. Let (X, Y ) be uniformly distributed on the unit disk {(x, y) : x2 +y2 = 1}. Let R = v X2 + Y 2. Find the cdf and pdf of R.