If able please provide some explanation with the following exercise, thank you in advance. i)Show that(Hint: Use the CLT for XnXi ~ Poi(1)).ii)(=lim en→∞-nnk!12k=01 X₁, where Xį are i.i.d. random variables such thatLet X₁,..., Xn be i.i.d independent Poisson random variables each havingmean 1 (i.e., Xį ~ Poi(1)). Let Sn := Σ₁ X₁. Using the above information, try to prove theStirling approximation:n! ≈ √√√2πn²+¹/2 e-n

We have to prove the following statement: limn→∞e-n∑k=0nnk/k!=0.5

Answered: i) Show that (Hint: Use the CLT for Xn…

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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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