Suppose that X₁,..., Xn is a random sample from a distribution with probability den- sity function 2 ) = { 1 - - - fx(x) = √3/₂e-x/0, 0 0. You are provided the information that the maximum likelihood estimator of is Ô = Σi=1 Xi 2n (You do not need to derive this mle.) (a) Verify that Fisher's information in the random sample is given by 2n In (0) 02

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Suppose that X₁,..., Xn is a random sample from a distribution with probability den-
sity function
2
) = { +/- - -
fx(x) =
√3/₂e-x/0, 0<x<∞,
otherwise,
where > 0.
You are provided the information that the maximum likelihood estimator of is
Ô
i=1
=
2n
(You do not need to derive this mle.)
(a) Verify that Fisher's information in the random sample is given by
2n
In (0)
02
Transcribed Image Text:Suppose that X₁,..., Xn is a random sample from a distribution with probability den- sity function 2 ) = { +/- - - fx(x) = √3/₂e-x/0, 0<x<∞, otherwise, where > 0. You are provided the information that the maximum likelihood estimator of is Ô i=1 = 2n (You do not need to derive this mle.) (a) Verify that Fisher's information in the random sample is given by 2n In (0) 02
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