Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Textbook Question
Chapter 6.6, Problem 64E
Refer to Exercise 6.63 and Example 6.14. Suppose that Y1 has a gamma distribution with parameters α1 and β, that Y1 is gamma distributed with parameters α2 and β, and that Y1 and Y2 are independent. Let U1 = Y1/(Y1 + Y2) and U2 = Y1 + Y2.
- a Derive the joint density
function for U1 and U2. - b Show that the marginal distribution of U1 is a beta distribution with parameters α1 and α2.
- c Show that the marginal distribution of U2 is a gamma distribution with parameters α = α1 + α2 and β.
- d Establish that U1 and U2 are independent.
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Chapter 6 Solutions
Mathematical Statistics with Applications
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