Let X1 and X2 have independent gamma distributions with parameters , and , , respectively. Let W = X1/(X1 + X2). Use a method similar to that given in the derivation of the F distribution (Example 5.2-4) to show that the pdf of W is g(w) = ( + ) ()() w1(1 w) 1, 0 < w < 1.We say that W has a beta distribution with parameters and . (See Example 5.2-3.)

Unit 4 Notes: Ethics of Experiments with Humans and Animals Week 3: 24 Jan 2018 Key Terms Key Terms 1. Voluntary response: a type of sampling that is not random and just uses a general call-out to get volunteers to participate 2. Informed consent: should be used in EVERY type of sample. The researcher can choose the sample, but the people chosen for the sample still need to give informed consent. Just because you’re chosen, doesn’t mean you have to participate 3. Replacement: use non-animal models such as microorganisms or cell culture techniques, computer simulations, or species lower on the phylogenetic scale 4. Reduction: reduce the numbers of animals needed by implementing