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1. (55 POINTS) Let X,...,X, be a random sample from Gamma(3,). Define the parameter n = Consider 1 and 2, two estimators for n:

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1. (55 POINTS) Let X,...,X, be a random sample from Gamma(3,). Define the parameter n = Consider 1 and 2, two estimators for n: = . -x/B n 12n =1 X, and ^2=(MLE) . f(x) = 17(3) [0,00) e. Determine the asymptotic distribution of a scaled version of 12. f. Which of the two sampling schemes would you recommend to a practitioner interested in obtaining good estimates of if the sample size is large? Justify your answer.

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