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i) Show that (Hint: Use the CLT for Xn Xį ~ Poi(1)). n Σ k=0 1 Xi, where X₁ are i.i.d. random variables such that * lim e-n n→∞ k! = 1 2

i) Show that (Hint: Use the CLT for Xn Xį ~ Poi(1)). n Σ k=0 1 Xi, where X₁ are i.i.d. random variables such that * lim e-n n→∞ k! = 1 2

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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If able please provide some explanation with the following exercise, thank you in advance.

i) Show that (Hint: Use the CLT for Xn Xi ~ Poi(1)). ii)( = lim e n→∞ -n n k! 1 2 k=0 1 X₁, where Xį are i.i.d. random variables such that Let X₁,..., Xn be i.i.d independent Poisson random variables each having mean 1 (i.e., Xį ~ Poi(1)). Let Sn := Σ₁ X₁. Using the above information, try to prove the Stirling approximation: n! ≈ √√√2πn²+¹/2 e-n
Transcribed Image Text:i) Show that (Hint: Use the CLT for Xn Xi ~ Poi(1)). ii)( = lim e n→∞ -n n k! 1 2 k=0 1 X₁, where Xį are i.i.d. random variables such that Let X₁,..., Xn be i.i.d independent Poisson random variables each having mean 1 (i.e., Xį ~ Poi(1)). Let Sn := Σ₁ X₁. Using the above information, try to prove the Stirling approximation: n! ≈ √√√2πn²+¹/2 e-n
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