“Mox–Buller”. Suppose we make a modification of the Box–Muller Algorithm A1 as follows. (1) Generate U, V independent uniform(0,1). (2) Deliver X = cos(2πU) −2 logV and Y = sin(2πV ) −2 log U. Find...

“Mox–Buller”. Suppose we make a modification of the Box–Muller Algorithm A1 as follows.

(1) Generate U, V independent uniform(0,1).

(2) Deliver X = cos(2πU) −2 logV and Y = sin(2πV ) −2 log U.

Find the marginal distributions of both X and Y ; then generate and plot a sample from the joint distribution. Are X and Y uncorrelated?