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Question 1 Let X ~ Pareto(r, 8) which has pdf: f(r) T > 8 > 0 and r > 1 (a) Given RS of size n from X, and assuming & is known. find the MLE for(h) Wha...

Question

Question 1 Let X ~ Pareto(r, 8) which has pdf: f(r) T > 8 > 0 and r > 1 (a) Given RS of size n from X, and assuming & is known. find the MLE for(h) What is the MLE for 8 ?HINT: $ dloes not depend on

Question 1 Let X ~ Pareto(r, 8) which has pdf: f(r) T > 8 > 0 and r > 1 (a) Given RS of size n from X, and assuming & is known. find the MLE for (h) What is the MLE for 8 ? HINT: $ dloes not depend on



Answers

Refer to Exercise $3.86 .$ The maximum likelihood estimator for $p$ is $1 / Y$ (note that $Y$ is the geometric random variable, not a particular value of it). Derive $E(1 / Y) .[\text { Hint: If }|r|<1$, $\left.\sum_{i=1}^{\infty} r^{i} / i=-\ln (1-r) .\right]$.


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