Suppose that a random variable X has the F distribution

Chapter 9, Problem 4

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QUESTION:

Suppose that a random variable X has the F distribution with m and n degrees of freedom (n > 2). Show that E(X) = n/(n 2). Hint: Find the value of E(1/Z), where Z has the 2 distribution with n degrees of freedom.

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QUESTION:

Suppose that a random variable X has the F distribution with m and n degrees of freedom (n > 2). Show that E(X) = n/(n 2). Hint: Find the value of E(1/Z), where Z has the 2 distribution with n degrees of freedom.

ANSWER:

Step 1 of 2

Let . Thus,. Thus,

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