For random variable w of example 410 we can generate random

Question

For random variable W of Example 4.10, we can generate random samples in two different ways:

1. Generate samples of X and Y and calculate W = Y/X.

2. Find the CDF F_W (w) and generate samples using Theorem 3.22.

Write Matlab functions w=wrv1(m) and w=wrv2(m) to implement these methods. Does one method run much faster? If so, why? (Use cputime to make run-time comparisons.)

Example 4.10

X and Y have the joint PDF

Find the PDF of W = Y/X

Theorem 3.22

Let U be a uniform (0, 1) random variable and let F(x) denote a cumulative distribution function with an inverse F ^-1(u) defined for 0 ^-1(U) has CDF FX (x) = F(x).