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Let the independent random variables X1 and X2 be N(0,1) and 2(r), respectively. Let Y1 = X1/X2/r and Y2 = X2. (a) Find the joint pdf of Y1 and Y2. (b) Determine the marginal pdf of Y1 and show that

Let the independent random variables X1 and X2 be N(0,1) and χ2(r), respectively. Let Y1 = X1/√X2/r and Y2 = X2.
(a) Find the joint pdf of Y1 and Y2.
(b) Determine the marginal pdf of Y1 and show that Y1 has a t distribution. (This is another, equivalent, way of finding the pdf of T.)

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a The joint pdf of X 1 and X 2 is …View the full answer


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Probability and Statistical Inference

Probability and Statistical Inference

ISBN: 978-0321923271

9th edition

Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

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Posted Date: October 12, 2015 08:50:26
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