1. Let Y have a chi-square distribution with 7 degrees of freedom. Find the following probabilities.
(a) P (Y > y0) = 0.025
(b) P (a <>Y < b)="">= 0.90
(c) P (Y > 1.239).
2. The time to failure T of a microwave oven has an exponential distribution with pdf 1 f(t) = 2 e- t/2, t > 0.
If three such microwave ovens are chosen and t is the mean of their failure times, ?nd the following:
(a) Distribution of T .
(b) P (T > 2).