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Let X> 0 and X, X₁, X2,... be random variables with X~ Poisson(A) and X₁ ~ Binom(n,A). Prove that {Xn}n>1 converges to X in distribution. You can assume that n is large enough such that < 1. n

Let X> 0 and X, X₁, X2,... be random variables with X~ Poisson(A) and X₁ ~ Binom(n,A). Prove that {Xn}n>1 converges to X in distribution. You can assume that n is large enough such that < 1. n

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 44CR
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Let X > 0 and X, X₁, X₂,... be random variables with X~ Poisson(X) and X₂ ~ Binom(n, Prove that {Xn}n>1 converges to X in distribution. You can assume that n is large enough such that < 1. n
Transcribed Image Text:Let X > 0 and X, X₁, X₂,... be random variables with X~ Poisson(X) and X₂ ~ Binom(n, Prove that {Xn}n>1 converges to X in distribution. You can assume that n is large enough such that < 1. n
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