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Let X₁, ...., X₁; i = 1,2, ... , n is a random sample from the Xn population with the probability mass function: f (x|0) = 0 (1 - 0)* ; x = 0,1,2,...0 < 0 <1 if it is known that parameter 8 has a prior beta probability function (3;4) as follows: T(7) h(0) = T(3)r (4) 1. determine the likelihood function L(x|0) 2. find the density function with X and 0, i.e. g(x|0) 3. find the posterior distribution for 0, i.e. k(0|x) 4. find the Bayesian estimator for 0, that is, T 0² (1 - 0)³ ; 0 <0 <1

Let X₁, ...., X₁; i = 1,2, ... , n is a random sample from the Xn population with the probability mass function: f (x|0) = 0 (1 - 0)* ; x = 0,1,2,...0 < 0 <1 if it is known that parameter 8 has a prior beta probability function (3;4) as follows: T(7) h(0) = T(3)r (4) 1. determine the likelihood function L(x|0) 2. find the density function with X and 0, i.e. g(x|0) 3. find the posterior distribution for 0, i.e. k(0|x) 4. find the Bayesian estimator for 0, that is, T 0² (1 - 0)³ ; 0 <0 <1

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.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 31CR
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Let X₁, ...., Xn; i = 1,2,..., n is a random sample from the population with the probability mass function: f (x|0) = 0 (1 - 0)* ; x = 0,1,2,... 0 <0 < 1 if it is known that parameter 0 has a prior beta probability function (3;4) as follows: T(7) h(0) = T(3)r (4) 1. determine the likelihood function L(x|0) 2. find the density function with X and 0, i.e. g(x|8) 3. find the posterior distribution for 0, i.e. k(0|x) 4. find the Bayesian estimator for 0, that is, T 0² (1-0)³ ; 0 <0 <1
Transcribed Image Text:Let X₁, ...., Xn; i = 1,2,..., n is a random sample from the population with the probability mass function: f (x|0) = 0 (1 - 0)* ; x = 0,1,2,... 0 <0 < 1 if it is known that parameter 0 has a prior beta probability function (3;4) as follows: T(7) h(0) = T(3)r (4) 1. determine the likelihood function L(x|0) 2. find the density function with X and 0, i.e. g(x|8) 3. find the posterior distribution for 0, i.e. k(0|x) 4. find the Bayesian estimator for 0, that is, T 0² (1-0)³ ; 0 <0 <1
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