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 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 Related to the proof of Fishers Theorem.
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Chapter1: Combinatorial Analysis
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[8.3]
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
Related to the proof of Fishers Theorem.
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