Refer to Exercise 6.63 and Example 6.14. Suppose that Y1 has a gamma distribution with
Chapter 6, Problem 6.64(choose chapter or problem)
Refer to Exercise 6.63 and Example 6.14. Suppose that Y1 has a gamma distribution with parameters 1 and , that Y1 is gamma distributed with parameters 2 and , 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 1 and 2. c Show that the marginal distribution of U2 is a gamma distribution with parameters = 1 + 2 and . d Establish that U1 and U2 are independent.
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