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Statistics / Probability and Statistics 4 / Chapter 7.6 / Problem 16

Probability and Statistics | 4th Edition | ISBN: 9780321500465 | Authors: Morris H. DeGroot, Mark J. Schervish

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Suppose that each of two statisticians A and B must

Chapter 7, Problem 16

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QUESTION:

Suppose that each of two statisticians A and B must estimate a certain parameter whose value is unknown ( > 0). Statistician A can observe the value of a random variable X, which has the gamma distribution with parameters and , where = 3 and = ; statistician B can observe the value of a random variable Y , which has the Poisson distribution with mean 2. Suppose that the value observed by statistician A is X = 2 and the value observed by statistician B is Y = 3. Show that the likelihood functions determined by these observed values are proportional, and find the common value of the M.L.E. of obtained by each statistician

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QUESTION:

Suppose that each of two statisticians A and B must estimate a certain parameter whose value is unknown ( > 0). Statistician A can observe the value of a random variable X, which has the gamma distribution with parameters and , where = 3 and = ; statistician B can observe the value of a random variable Y , which has the Poisson distribution with mean 2. Suppose that the value observed by statistician A is X = 2 and the value observed by statistician B is Y = 3. Show that the likelihood functions determined by these observed values are proportional, and find the common value of the M.L.E. of obtained by each statistician

ANSWER:

Step 1 of 6

Let random variables have joint pdf or pmb

where the parameters are unknown. When function is a function of parameters , it is called the likelihood function

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