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) = 1(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,...., 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) = 1(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
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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Please answer number 3
![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) (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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08d88023-a718-42ce-b92b-864b4cd943ff%2F4220b7ee-1863-4123-8e72-e3522272d450%2Fl2ddg6q_processed.jpeg&w=3840&q=75)
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) (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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