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) Z+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 + Z₂)²/2 + (Z₁-Z₂)²/2 (b) Z+Z2 Related to the proof of Fishers Theorem.
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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
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(b) Z² + Z2²2/0
Related to the proof of Fishers Theorem.
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