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Deriving the Maximum Likelihood Estimator point possible (graded) We use the same statistical set-up as above. Recall that Pe is the pmf of Pe and Xi,- "Xn id ...

Question

Deriving the Maximum Likelihood Estimator point possible (graded) We use the same statistical set-up as above. Recall that Pe is the pmf of Pe and Xi,- "Xn id Pa . Suppose that Omin is minimizer for the function f(0) (pe (X;)) Which of the following functions is also minimized at Bmin =-IIEiPe (X;) = 25 _ IIi1 Pe (X;) =h(0* ) - ITi-Pe (X;) where h is function of @* that does not depend on 0. 94 (0) =0 _ IIF1Pe (X;) All of the above =-4Zb(

Deriving the Maximum Likelihood Estimator point possible (graded) We use the same statistical set-up as above. Recall that Pe is the pmf of Pe and Xi,- "Xn id Pa . Suppose that Omin is minimizer for the function f(0) (pe (X;)) Which of the following functions is also minimized at Bmin =-IIEiPe (X;) = 25 _ IIi1 Pe (X;) =h(0* ) - ITi-Pe (X;) where h is function of @* that does not depend on 0. 94 (0) =0 _ IIF1Pe (X;) All of the above =-4Zb(



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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