a. Let T be an exponential random variable with parameter
Chapter , Problem 42(choose chapter or problem)
a. Let T be an exponential random variable with parameter \(\lambda\); let W be a random variable independent of T, which is \(\pm 1\) with probability \(\frac{1}{2}\) each; and let X = WT. Show that the density of X is
\(f_{X}(x)=\frac{\lambda}{2} e^{-\lambda|x|}\)
which is called the double exponential density.
b. Show that for some constant c,
\(\frac{1}{\sqrt{2 \pi}} e^{-x^{2} / 2} \leq c e^{-|x|}\)
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.
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer