Homework10 - Y = X 1 X 2 3 Let X have a t-distribution with...

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ST561 Fall 2010 Homework 10 Due: Wed, Dec. 8th, 2010 1. Let X j , j = 1 , 2 , 3 are independent with X j having a gamma distribution with param- eter α j and 1. Let Y 1 = X 1 X 1 + X 2 + X 3 , Y 2 = X 2 X 1 + X 2 + X 3 , Y 3 = X 1 + X 2 + X 3 . Find the joint distribution of ( Y 1 , Y 2 , Y 3 ). Are the transformed variables independent? 2. Let X 1 and X 2 be independent, with X 1 having an Exp (1) distribution and X 2 a Uniform(0,1) distribution. Find the p.d.f. of
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Unformatted text preview: Y = X 1 + X 2 . 3. Let X have a t-distribution with p degrees of freedom. Show that X 2 has a F-distribution with 1 and p degrees of freedom. 4. Let S 2 be the sample variance of a random sample of size 6 from a N ( μ, 12) distribution. Find P (2 . 30 < S 2 < 22 . 2). 1...
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