If Y is a random variable that has an F distribution with

Chapter 7, Problem 29E

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QUESTION:

Problem 29E

If Y is a random variable that has an F distribution with ν1 numerator and ν2 denominator degrees of freedom, show that U = 1/Y has an F distribution with ν2 numerator and ν1 denominator degrees of freedom.

        

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QUESTION:

Problem 29E

If Y is a random variable that has an F distribution with ν1 numerator and ν2 denominator degrees of freedom, show that U = 1/Y has an F distribution with ν2 numerator and ν1 denominator degrees of freedom.

        

ANSWER:

Step 1 of 2

Let  and  follows chi-square distribution with  degree of freedom respectively.

The F-ratio is defined as:

             

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