Question: Let Y have the F distribution with m and n degrees of freedom. We wish to estimate Pr(Y > c). Consider the p.d.f. a. Explain

Let Y have the F distribution with m and n degrees of freedom. We wish to estimate Pr(Y > c). Consider the p.d.f.

a. Explain how to simulate pseudo-random numbers with the p.d.f. f .
b. Explain how to estimate Pr(Y > c) using importance sampling with the importance function f .
c. Look at the form of the p.d.f. of Y, Eq. (9.7.2), and explain why importance sampling might be more efficient than sampling i.i.d. F random variables with m and n degrees of freedom if c is not small.

n/2)Cn/2 0 f(x)= otherwise

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