Question: Let X1. X3. ..... Y n be a random sample from a discrete um'fonn population with probability density function I f(.')= .1'=l,2,...,3, Where 9 is

Let X1. X3. ..... Y n be a random sample from a discrete um'fonn population with probability density function I f(.\\')= .1'=l,2,...,3, Where 9 is a positive unknown integer parameter. (a) Find the method of moments estimator of 9. to) Determine whether the method of moments estimator of 9 is an unbiased estimmm- of 9. (cl Find the population variance of the method of moments estimator of 9. (d) Discuss any problems that you can see with the method of moments estimator. Hint: consider the data set 1. 2, 9. (e) Find the maximum likelihood estimator of 6. (f) Give a formula for the likelihood ratio test statistic for testing Ho:9=20 versus H1 : e

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