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Q 8.3. Suppose Z₁, Z2 and Z3 are independent standard (univariate) normal random variables. Which of the following have a x²-distribution (and for these identify the degrees of freedom)? (Hint: you should not have to do a lot of calculations.) (a) (Z₁ - 2Z2 + Z3)²/6 + (Z₁ − Z3)²/2 (b) (Z₁ + Z2 + Z3)²/3 (c) (Z₁ + Z₂)²/2 (d) (Z₁ + Z₂)²/2 + (Z₁ − Z₂)²/2 (e) Z1 + Z² Related to the proof of Fishers Theorem.

Q 8.3. Suppose Z₁, Z2 and Z3 are independent standard (univariate) normal random variables. Which of the following have a x²-distribution (and for these identify the degrees of freedom)? (Hint: you should not have to do a lot of calculations.) (a) (Z₁ - 2Z2 + Z3)²/6 + (Z₁ − Z3)²/2 (b) (Z₁ + Z2 + Z3)²/3 (c) (Z₁ + Z₂)²/2 (d) (Z₁ + Z₂)²/2 + (Z₁ − Z₂)²/2 (e) Z1 + Z² Related to the proof of Fishers Theorem.

MATLAB: An Introduction with Applications
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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Q 8.3. Suppose Z₁, Z2 and Z3 are independent standard (univariate) normal random variables. Which of the following have a x²-distribution (and for these identify the degrees of freedom)? (Hint: you should not have to do a lot of calculations.) (a) (Z₁ − 2Z2 + Z3)²/6 + (Z1 − Z3)²/2 (b) (Z₁ + Z2 + Z3)²/3 (c) (Z₁ + Z₂)²/2 (d) (Z₁ + Z₂)²/2 + (Z₁ − Z₂)²/2 (e) Z1 + Z² Related to the proof of Fishers Theorem.
Transcribed Image Text:Q 8.3. Suppose Z₁, Z2 and Z3 are independent standard (univariate) normal random variables. Which of the following have a x²-distribution (and for these identify the degrees of freedom)? (Hint: you should not have to do a lot of calculations.) (a) (Z₁ − 2Z2 + Z3)²/6 + (Z1 − Z3)²/2 (b) (Z₁ + Z2 + Z3)²/3 (c) (Z₁ + Z₂)²/2 (d) (Z₁ + Z₂)²/2 + (Z₁ − Z₂)²/2 (e) Z1 + Z² Related to the proof of Fishers Theorem.
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