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Homework10
Course: ST 561, Fall 2010School: Oregon State University
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2010 Homework ST561 Fall 10 Due: Wed, Dec. 8th, 2010 1. Let Xj , j = 1, 2, 3 are independent with Xj having a gamma distribution with parameter j and 1. Let Y1 = X2 X1 , Y2 = , Y3 = X1 + X2 + X3 . X1 + X2 + X3 X1 + X2 + X3 Find the joint distribution of (Y1 , Y2 , Y3 ). Are the transformed variables independent? 2. Let X1 and X2 be independent, with X1 an having Exp(1) distribution and X2 a Uniform(0,1)...
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2010
Homework ST561
Fall 10
Due: Wed, Dec. 8th, 2010
1. Let Xj , j = 1, 2, 3 are independent with Xj having a gamma distribution with parameter j and 1. Let Y1 = X2 X1 , Y2 = , Y3 = X1 + X2 + X3 . X1 + X2 + X3 X1 + X2 + X3
Find the joint distribution of (Y1 , Y2 , Y3 ). Are the transformed variables independent? 2. Let X1 and X2 be independent, with X1 an having Exp(1) distribution and X2 a Uniform(0,1) distribution. Find the p.d.f. of Y = X1 + X2 . 3. Let X have a t-distribution with p degrees of freedom. Show that X 2 has a Fdistribution 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 (, 12) distribution. Find P (2.30 < S 2 < 22.2).
1
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Oregon State University - ST - 561
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Oregon State University - ST - 561
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Oregon State University - ST - 561
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Oregon State University - ST - 561
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Oregon State University - ST - 561
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Oregon State University - ST - 561
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Oregon State University - ST - 561
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Oregon State University - ST - 561
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Oregon State University - ST - 561
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Oregon State University - ST - 561
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Oregon State University - ST - 561
Oregon State University - ST - 561
Oregon State University - ST - 561
Oregon State University - ST - 561
Oregon State University - ST - 561
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Oregon State University - ECE - 468
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Oregon State University - ECE - 468
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Oregon State University - ECE - 468
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Oregon State University - ECE - 468
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