Let X 1 ,X 2 ,X 3 ,X 4 be a random sample of size n 4 from the normal distribution N(0,1) Show that 4 i 1 (X i X) 2 equals and argue that these three terms are independent, each with a chi square distribution with 1 degree of freedom (XX) X3 (X X) 2 X (X X2 X3) 3 2 3 2 4 3...

4i1Xi X2 4i1Xi2 2X4i1Xi X24 4i1Xi2 4X2 4i1Xi ...

Let X 1 ,X 2 ,X 3 ,X 4 be a random sample of size n =

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Let X₁,X₂,X₃,X₄ be a random sample of size n = 4 from the normal distribution N(0,1). Show that Σ⁴_i=1(X_i − ‾X)² equals

and argue that these three terms are independent, each with a chi-square distribution with 1 degree of freedom.

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Introduction To Mathematical Statistics

ISBN: 9780321794710

7th Edition

Authors: Robert V., Joseph W. McKean, Allen T. Craig

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Question Posted: Oct 17, 2022 04:07 AM

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Let X 1 ,X 2 ,X 3 ,X 4 be a random sample of size n =

Question:

(X₁X₂)² [X3 - (X₁ + X₂)/2]² [X₁-(X₁ + X2 + X3)/3]² +. + 2 3/2 4/3

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Introduction To Mathematical Statistics

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