Suppose that Yhas a x2 distribution with v degrees of freedom. Use the results in Exercise 4.111 in your answers to the following. These results will be useful when we study the tand F distributions in Chapter 7. a Give an expression for E(Ya) if v >-2a. b Why did your answer in part (a) require that v>-2a? c Use the result in part (a) to give an expression for E(Y). What do you need to assume about v? d Use the result in part (a) to give an expression for E(1/Y), E(1/√ Y), and E(1/Y2). What do you need to assume about v in each case? Reference Suppose that Yhas a gamma distribution with parameters a and B. a If a is any positive or negative value such that a + a>0, show that E(Yª): = Bar (a + a) Γ(α) b Why did your answer in part (a) require that a + a > 0? c Show that, with a = 1, the result in part (a) gives E(Y) = aß. d Use the result in part (a) to give an expression for E(√ Y). What do you need to assume about a? e Use the result in part (a) to give an expression for E(1/Y), E(1/√ Y), and E(1/Y2). What do you need to assume about a in each case?

Suppose that Yhas a x2 distribution with v degrees of freedom. Use the results in Exercise 4.111 in your answers to the following. These results will be useful when we study the tand F distributions in Chapter 7. a Give an expression for E(Ya) if v >-2a. b Why did your answer in part (a) require that v>-2a? c Use the result in part (a) to give an expression for E(Y). What do you need to assume about v? d Use the result in part (a) to give an expression for E(1/Y), E(1/√ Y), and E(1/Y2). What do you need to assume about v in each case? Reference Suppose that Yhas a gamma distribution with parameters a and B. a If a is any positive or negative value such that a + a>0, show that E(Yª): = Bar (a + a) Γ(α) b Why did your answer in part (a) require that a + a > 0? c Show that, with a = 1, the result in part (a) gives E(Y) = aß. d Use the result in part (a) to give an expression for E(√ Y). What do you need to assume about a? e Use the result in part (a) to give an expression for E(1/Y), E(1/√ Y), and E(1/Y2). What do you need to assume about a in each case?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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