In Example 2c we simulated the absolute value of a unit normal by using the rejection proc...

In Example 2c we simulated the absolute value of a unit normal by using the rejection procedure on exponential random variables with rate 1. This raises the question of whether we could obtain a more efficient algorithm by using a different exponential density–that is, we could use the density g(x) = Show that the mean number of iterations needed in the rejection scheme is minimized when .