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 + Z₂)²/2 + (Z₁-Z₂)²/2 (b) Z² + Z2

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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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 + Z₂)²/2 + (Z₁ – Z₂)²/2
(b) Z1 + Z2
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 + Z₂)²/2 + (Z₁ – Z₂)²/2 (b) Z1 + Z2
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