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9.43 Let Y₁, Y₂,..., Y₁ denote independent and identically distributed random variables from a power family distribution with parameters a and 0. Then, by the result in Exercise 6.17, if a, 0 > 0, f(y|a, 0) = [aya-1/0°, 0₁. If is known, show that I Y; is sufficient for a. 0≤ y ≤0, elsewhere.

9.43 Let Y₁, Y₂,..., Y₁ denote independent and identically distributed random variables from a power family distribution with parameters a and 0. Then, by the result in Exercise 6.17, if a, 0 > 0, f(y|a, 0) = [aya-1/0°, 0₁. If is known, show that I Y; is sufficient for a. 0≤ y ≤0, elsewhere.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.4: Discrete Random Variables; Applications To Decision Making
Problem 15E
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Answer 9.43

9.43 Let Y₁, Y₂,..., Y₁ denote independent and identically distributed random variables from a power family distribution with parameters a and 0. Then, by the result in Exercise 6.17, if a, 0 > 0, f(y|a, 0) = [aya-1/0°, 0₁. If is known, show that I Y; is sufficient for a. 0≤ y ≤0, elsewhere.
Transcribed Image Text:9.43 Let Y₁, Y₂,..., Y₁ denote independent and identically distributed random variables from a power family distribution with parameters a and 0. Then, by the result in Exercise 6.17, if a, 0 > 0, f(y|a, 0) = [aya-1/0°, 0₁. If is known, show that I Y; is sufficient for a. 0≤ y ≤0, elsewhere.
6.17 A member of the power family of distributions has a distribution function given by y < 0, 0 ≤ y ≤0, y > 0, where a, 0 > 0. ctions of Random Variables F(x) = a Find the density function. b 0, G). hts Reserved. May not be copied, seamed, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChap d content does not materially affect the overall learning experience. Cengage Leaming reserves the right to remove additional content at any time if subsequent rights restriction 1, For fixed values of a and , find a transformation G(U) so that G(U) has a distribution function of F when U possesses a uniform (0, 1) distribution. c Given that a random sample of size 5 from a uniform distribution on the interval (0, 1) yielded the values .2700, .6901, .1413, .1523, and .3609, use the transformation derived in part (b) to give values associated with a random variable with a power family distribution with a? A
Transcribed Image Text:6.17 A member of the power family of distributions has a distribution function given by y < 0, 0 ≤ y ≤0, y > 0, where a, 0 > 0. ctions of Random Variables F(x) = a Find the density function. b 0, G). hts Reserved. May not be copied, seamed, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChap d content does not materially affect the overall learning experience. Cengage Leaming reserves the right to remove additional content at any time if subsequent rights restriction 1, For fixed values of a and , find a transformation G(U) so that G(U) has a distribution function of F when U possesses a uniform (0, 1) distribution. c Given that a random sample of size 5 from a uniform distribution on the interval (0, 1) yielded the values .2700, .6901, .1413, .1523, and .3609, use the transformation derived in part (b) to give values associated with a random variable with a power family distribution with a? A
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