a. Let T be an exponential random variable with parameter λ; let W be a random varia...

a. Let T be an exponential random variable with parameter λ; let W be a random variable independent of T , which is ±1 with probability 1/ 2 each; and let X = WT. Show that the density of X is

which is called the double exponential density.

b. Show that for some constant c,

Use this result and that of part (a) to show how to use the rejection method to generate random variables from a standard normal density.