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2. Let X₁, X2, Xn represent a random sample from a Poisson distribution with probability mass function given below. p(x) = = e X = = 0, 1, 2, ... (a) Look up the Special Distributions summary sheet on Moodle and state E(X). (b) Find the moment estimator of X. (c) Show that the maximum likelihood estimator of A is the same as the moment estimator. x! " (d) Estimate from the following observations using the moment/maximum likelihood estimator. Round your answer to 4 decimal places. X 0 1 2 3 4 567 Frequency 18 37 42 30 13 7 2 1

2. Let X₁, X2, Xn represent a random sample from a Poisson distribution with probability mass function given below. p(x) = = e X = = 0, 1, 2, ... (a) Look up the Special Distributions summary sheet on Moodle and state E(X). (b) Find the moment estimator of X. (c) Show that the maximum likelihood estimator of A is the same as the moment estimator. x! " (d) Estimate from the following observations using the moment/maximum likelihood estimator. Round your answer to 4 decimal places. X 0 1 2 3 4 567 Frequency 18 37 42 30 13 7 2 1

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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2. Let X₁, X2, ..., Xn represent a random sample from a Poisson distribution with probability mass function given below. p(x) = e-11e0 el x! summary sheet on Moodle and state E(X). X 2 (a) Look up the Special Distributions (b) Find the moment estimator of X. (c) Show that the maximum likelihood estimator of X is the same as the moment estimator. x = 0, 1, 2, ... (d) Estimate A from the following observations using the moment/maximum likelihood. estimator. Round your answer to 4 decimal places. Frequency 18 0 1 2 3 4 5 6 7 37 42 30 13 7 2 1
Transcribed Image Text:2. Let X₁, X2, ..., Xn represent a random sample from a Poisson distribution with probability mass function given below. p(x) = e-11e0 el x! summary sheet on Moodle and state E(X). X 2 (a) Look up the Special Distributions (b) Find the moment estimator of X. (c) Show that the maximum likelihood estimator of X is the same as the moment estimator. x = 0, 1, 2, ... (d) Estimate A from the following observations using the moment/maximum likelihood. estimator. Round your answer to 4 decimal places. Frequency 18 0 1 2 3 4 5 6 7 37 42 30 13 7 2 1
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