Let X1 and X2 be independent chi-square random variables

Chapter 5, Problem 2E

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QUESTION:

Problem 2E

Let X1 and X2 be independent chi-square random variables with r1 and r2 degrees of freedom, respectively. Let Y1 = (X1/r1)/(X2/r2) and Y2 = X2.

(a) Find the joint pdf of Y1 and Y2.

(b) Determine the marginal pdf of Y1 and show that Y1 has an F distribution. (This is another, but equivalent, way of finding the pdf of F.)

Questions & Answers

QUESTION:

Problem 2E

Let X1 and X2 be independent chi-square random variables with r1 and r2 degrees of freedom, respectively. Let Y1 = (X1/r1)/(X2/r2) and Y2 = X2.

(a) Find the joint pdf of Y1 and Y2.

(b) Determine the marginal pdf of Y1 and show that Y1 has an F distribution. (This is another, but equivalent, way of finding the pdf of F.)

ANSWER:

Step 1 of 3

Given:

  and  are independent chi-square random variables with   and  degrees of freedom.

                                                                      

                                                                           

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