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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 FW (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).
the article modeling sediment and water column interactions for hydrophobic pollutants water research 1984 1169-1174
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