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Question 1 Let X₁, X, be an i.i.d. sample from the distribution with probability mass func- tion Pr(x = k) = p(1-p)-1, for k= (1,2,3,... } and p = (0, 1). For all i, we have E(X;) = 1/p. (You don't need to prove this.) (a) Find a method of moments estimator of p. (b) Find a maximum likelihood estimator of p. Show carefully that it corresponds to a maximum of the likelihood function

Question 1 Let X₁, X, be an i.i.d. sample from the distribution with probability mass func- tion Pr(x = k) = p(1-p)-1, for k= (1,2,3,... } and p = (0, 1). For all i, we have E(X;) = 1/p. (You don't need to prove this.) (a) Find a method of moments estimator of p. (b) Find a maximum likelihood estimator of p. Show carefully that it corresponds to a maximum of the likelihood function

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question 1 tion Let X₁, X₂, be an i.i.d. sample from the distribution with probability mass func- Pr(X= k) = p(1-p)-1, for k = {1,2,3,...} and p = (0, 1). For all i, we have E(X;)=1/p. (You don't need to prove this.) (a) Find a method of moments estimator of p. (b) Find a maximum likelihood estimator of p. Show carefully that it corresponds to a maximum of the likelihood function.
Transcribed Image Text:Question 1 tion Let X₁, X₂, be an i.i.d. sample from the distribution with probability mass func- Pr(X= k) = p(1-p)-1, for k = {1,2,3,...} and p = (0, 1). For all i, we have E(X;)=1/p. (You don't need to prove this.) (a) Find a method of moments estimator of p. (b) Find a maximum likelihood estimator of p. Show carefully that it corresponds to a maximum of the likelihood function.
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