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Consider the sample X = {X₁, ..., Xn} of n i.i.d. Poisson random variables with parameter A. (a) Find the maximum likelihood for X and its asymptotic sampling distribution. Find the MLE for the parameter μ = e = e-\. (b) Suppose now that, rather than observing the actual values of the random variables Xi, we are just able to register whether they are null or positive (i.e. we have censored observations). More precisely, only the events X₁ = 0 or X₂ > 0 for i = 1,...,n are observed. Find the maximum likelihood estimator for X for these new observations.

Consider the sample X = {X₁, ..., Xn} of n i.i.d. Poisson random variables with parameter A. (a) Find the maximum likelihood for X and its asymptotic sampling distribution. Find the MLE for the parameter μ = e = e-\. (b) Suppose now that, rather than observing the actual values of the random variables Xi, we are just able to register whether they are null or positive (i.e. we have censored observations). More precisely, only the events X₁ = 0 or X₂ > 0 for i = 1,...,n are observed. Find the maximum likelihood estimator for X for these new observations.

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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= Consider the sample X = (a) (b) {X₁,..., Xn} of n i.i.d. Poisson random variables with parameter X. Find the maximum likelihood for X and its asymptotic sampling distribution. Find the MLE for the parameter μ = e =e=^. Suppose now that, rather than observing the actual values of the random variables Xį, we are just able to register whether they are null or positive (i.e. we have censored observations). More precisely, only the events Xį = 0 or X₂ > 0 for i = 1,..., n are observed. (c) Find the maximum likelihood estimator for X for these new observations.
Transcribed Image Text:= Consider the sample X = (a) (b) {X₁,..., Xn} of n i.i.d. Poisson random variables with parameter X. Find the maximum likelihood for X and its asymptotic sampling distribution. Find the MLE for the parameter μ = e =e=^. Suppose now that, rather than observing the actual values of the random variables Xį, we are just able to register whether they are null or positive (i.e. we have censored observations). More precisely, only the events Xį = 0 or X₂ > 0 for i = 1,..., n are observed. (c) Find the maximum likelihood estimator for X for these new observations.
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