6. In Example 11.4 we simulated the absolute value of a standard normal by using the Von Neumann 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) =

λe−λx. Show that the mean number of iterations needed in the rejection scheme is minimized when λ = 1.