1. Let X and Y be independent random variables from an exponential distribution with common parameter θ = 1. Show that X/Y has an F -distribution. What is the number for degrees of freedom?
2. Let X be F distributed with 9 numerator and 12 denominator degrees of freedom. Find
(a) P (X ≤ 3.87),
(b) P (X ≤ 0.196),
(c) The value of a and b such that P (a <>Y < b)="">= 0.95.