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Let X1, X2, X3, and X4 be independent Poisson random variables, with parameters A₁ = 3A, A2 = A, A3 = 9A, and A4 = 4A, respectively. (a) Find and simplify the joint pmf f(x1, x2, x3, x4; A1, A2, A3, A4). (b) Find L(A) and (A), the likelihood and log-likelihood functions.

Let X1, X2, X3, and X4 be independent Poisson random variables, with parameters A₁ = 3A, A2 = A, A3 = 9A, and A4 = 4A, respectively. (a) Find and simplify the joint pmf f(x1, x2, x3, x4; A1, A2, A3, A4). (b) Find L(A) and (A), the likelihood and log-likelihood functions.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 22E
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(c) Find A, the maximum likelihood estimator for A. (You do not need to prove that your solution is a max). (d) Show that your estimator X from (c) is an unbiased estimator of X.
Transcribed Image Text:(c) Find A, the maximum likelihood estimator for A. (You do not need to prove that your solution is a max). (d) Show that your estimator X from (c) is an unbiased estimator of X.
Let X1, X2, X3, and X4 be independent Poisson random variables, with parameters A₁ = 3A, A2 = A, A3 = 9A, and A4 = 4A, respectively. (a) Find and simplify the joint pmf f(x1, x2, x3, x4; A1, A2, A3, A4). (b) Find L(A) and (A), the likelihood and log-likelihood functions.
Transcribed Image Text:Let X1, X2, X3, and X4 be independent Poisson random variables, with parameters A₁ = 3A, A2 = A, A3 = 9A, and A4 = 4A, respectively. (a) Find and simplify the joint pmf f(x1, x2, x3, x4; A1, A2, A3, A4). (b) Find L(A) and (A), the likelihood and log-likelihood functions.
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