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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?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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Suppose that Yhas a x ² 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?
Transcribed Image Text:Suppose that Yhas a x ² 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?
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