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Question [12 pts]Let X1;Xz;- Xn be random sample from gamma population with parameters where 1S5 known with pdfand 8=f(i;a,8) = 1" - e-r/a, BoT(a) for I > 0...

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Question [12 pts]Let X1;Xz;- Xn be random sample from gamma population with parameters where 1S5 known with pdfand 8=f(i;a,8) = 1" - e-r/a, BoT(a) for I > 0, a > 0, 8 > 0. Find maximum likelihood estimators (MLEs ) for(ii) t = (28 _ 1)2.Show that MLE 3 is efficient estimator of 8. Find the asymptotic distribution of Vn(f where is definedpartabove

Question [12 pts] Let X1;Xz;- Xn be random sample from gamma population with parameters where 1S5 known with pdf and 8= f(i;a,8) = 1" - e-r/a, BoT(a) for I > 0, a > 0, 8 > 0. Find maximum likelihood estimators (MLEs ) for (ii) t = (28 _ 1)2. Show that MLE 3 is efficient estimator of 8. Find the asymptotic distribution of Vn(f where is defined part above



Answers

Identify the probability density function. Then find the mean, variance, and standard deviation without integrating. $$ f(x)=\frac{1}{8} e^{-x / 8},[0, \infty) $$


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