# 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.)

(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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**Related Book For**

## Probability and Statistical Inference

**ISBN:** 978-0321923271

9th edition

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

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