Solution Found!
Let X1 and X2 be independent chi-square random variables
Chapter 5, Problem 2E(choose chapter or problem)
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.