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Let X Poi(A), a Poisson distribution with parameter > 0. This is a discrete probability distribution on the non-negative integers, with p.m.f. given by fx (k): - Xk k! e 9 k = 0, 1, 2,... (i) Verify (by calculation) that the log-likelihood function for the parameter X is given by l(x; λ) = n(x log A - A) - log(x₁!x₂!· · · xn!). (ii) Derive the MLE estimator for A, and use it to compute the MLE estimate for the following sample data 5: 1 3 2 3 3 0 3 3 5 2 3 4 3 (iii) Is the MLE estimator found in the last part unbiased? Justify your answer.

Let X Poi(A), a Poisson distribution with parameter > 0. This is a discrete probability distribution on the non-negative integers, with p.m.f. given by fx (k): - Xk k! e 9 k = 0, 1, 2,... (i) Verify (by calculation) that the log-likelihood function for the parameter X is given by l(x; λ) = n(x log A - A) - log(x₁!x₂!· · · xn!). (ii) Derive the MLE estimator for A, and use it to compute the MLE estimate for the following sample data 5: 1 3 2 3 3 0 3 3 5 2 3 4 3 (iii) Is the MLE estimator found in the last part unbiased? Justify your answer.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Let X~ Poi(), a Poisson distribution with parameter > 0. This is a discrete probability distribution on the non-negative integers, with p.m.f. given by fx(k) = Xk k! -1 9 k = 0, 1, 2, ... (i) Verify (by calculation) that the log-likelihood function for the parameter λ is given by l(x; λ) = n(x log A - A) - log(x₁!x₂!· · · xn!). (ii) Derive the MLE estimator for λ, and use it to compute the MLE estimate for the following sample data 75: 1 3 2 3 3 0 3 3 5 2 3 4 3 (iii) Is the MLE estimator found in the last part unbiased? Justify your answer.
Transcribed Image Text:Let X~ Poi(), a Poisson distribution with parameter > 0. This is a discrete probability distribution on the non-negative integers, with p.m.f. given by fx(k) = Xk k! -1 9 k = 0, 1, 2, ... (i) Verify (by calculation) that the log-likelihood function for the parameter λ is given by l(x; λ) = n(x log A - A) - log(x₁!x₂!· · · xn!). (ii) Derive the MLE estimator for λ, and use it to compute the MLE estimate for the following sample data 75: 1 3 2 3 3 0 3 3 5 2 3 4 3 (iii) Is the MLE estimator found in the last part unbiased? Justify your answer.
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