2. Dene the random variable X as the time (in months) a jet engine can operate before needing to be rebuilt. The cumulative distribution function F(x) (P(X S 23)) is given to be: 0 2750 F(m) = 1.2 1 exp (0.03m1'2) = 1 _ 80.03m x > 0 a. What is the PIObability that a jet engine will last less than 12 months before needing to be rebuilt? b. What is the probability that a jet engine will last more than 12 months before needing to be rebuilt? 0. Given a jet engine has lasted more than 6 months, what is the probability it will last more than 12 months before needing a rebuild? (hint: P (AIB) = P_(1(;4QBT).)