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

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

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.CR: Chapter 13 Review

Problem 43CR

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8、3

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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