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Show that for any &> 0 and Sn = 1X₁, lim P(|S₁ − 0| ≥ ɛ) = 0. n-00

Show that for any &> 0 and Sn = 1X₁, lim P(|S₁ − 0| ≥ ɛ) = 0. n-00

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Suppose that a sequence of mutually independent and identically distributed discrete random variables X₁, X₂, X3,..., Xn has the following probability density function 0xe-0 x! 0, f(x; 0) = for x = 0,1,2,... elsewhere a) Show that for any & > 0 and S₁ = =-=₁ X₁, lim P(|S, − 0| ≥ ɛ) = 0. =1 n2-00
Transcribed Image Text:Suppose that a sequence of mutually independent and identically distributed discrete random variables X₁, X₂, X3,..., Xn has the following probability density function 0xe-0 x! 0, f(x; 0) = for x = 0,1,2,... elsewhere a) Show that for any & > 0 and S₁ = =-=₁ X₁, lim P(|S, − 0| ≥ ɛ) = 0. =1 n2-00
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