Let the sequence of n random variables {X₁, X2,..., Xn}, independently obtained from some probability density function px (x). If E[X₂] = μ and Var(X₂) = o² are finite then, as n increases to infinity, according to the Central Limit Theorem the random variable S = √4n(Xn-μ) approaches which distribution? Justify its type (name), and hence compute its mean and variance.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Let the sequence of n random variables {X₁, X2,..., Xn}, independently obtained from
some probability density function px (x). If E[X₂] = μ and Var(X₂) = o² are finite then,
as n increases to infinity, according to the Central Limit Theorem the random variable
S = √4n(Xn-μ) approaches which distribution? Justify its type (name), and hence
compute its mean and variance.
Transcribed Image Text:Let the sequence of n random variables {X₁, X2,..., Xn}, independently obtained from some probability density function px (x). If E[X₂] = μ and Var(X₂) = o² are finite then, as n increases to infinity, according to the Central Limit Theorem the random variable S = √4n(Xn-μ) approaches which distribution? Justify its type (name), and hence compute its mean and variance.
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