4. Let X₁, X₂,..., X, be mutually independent and identically distributed random variables with means μ and variance o². Let X = (X)/n. Show that n n Σ(X-X)² =Σ(Xx μ)² n(X μ)² k=1 k=1

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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4. Let X₁, X₂,..., X, be mutually independent and identically distributed random
variables with means μ and variance o². Let X = (X)/n. Show that
72
n
Σ(X₂-X)² = Σ(Xx-μ)² n(X-μ)²
k=1
k=1
Transcribed Image Text:4. Let X₁, X₂,..., X, be mutually independent and identically distributed random variables with means μ and variance o². Let X = (X)/n. Show that 72 n Σ(X₂-X)² = Σ(Xx-μ)² n(X-μ)² k=1 k=1
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