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X; has a Poisson distribution with mean Let X₁, X2, ..., X₁, be a random sample from a Poisson distribution with mean λ. Thus, Y = nλ. Moreover, by the Central limit Theorem, X = Y/n has, approximately, a Normal (A, λ/n) distribution for large n. Show that for large values of n, the distribution of is independent of λ. 2 √ ( √= -√A) n

X; has a Poisson distribution with mean Let X₁, X2, ..., X₁, be a random sample from a Poisson distribution with mean λ. Thus, Y = nλ. Moreover, by the Central limit Theorem, X = Y/n has, approximately, a Normal (A, λ/n) distribution for large n. Show that for large values of n, the distribution of is independent of λ. 2 √ ( √= -√A) n

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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Let X₁, X₂, ..., X₁, be a random sample from a Poisson distribution with mean . Thus, Y = Σ₁ X; has a Poisson distribution with mean nλ. Moreover, by the Central limit Theorem, X = Y/n has, approximately, a Normal (A, λ/n) distribution for large n. Show that for large values of n, the distribution of 2 √² ( √= -√ā) is independent of λ.
Transcribed Image Text:Let X₁, X₂, ..., X₁, be a random sample from a Poisson distribution with mean . Thus, Y = Σ₁ X; has a Poisson distribution with mean nλ. Moreover, by the Central limit Theorem, X = Y/n has, approximately, a Normal (A, λ/n) distribution for large n. Show that for large values of n, the distribution of 2 √² ( √= -√ā) is independent of λ.
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