1. Define the random variable X as the time (in months) a jet engine can operate...

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1. Define 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 x)) is given to be: F(x) { 0 < 0 exp(-0.03x1.2) = 1 e0.03x1.2 x > 0 a. What is the probability that a jet engine will last less than 12 months before needing to be rebuilt? rior Sev b. What is the probability that a jet engine will last more than 12 months before needing to be rebuilt? c. 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? d. Find the 50-th percentile of X. That is to say the value of x such that P(X x) = 0.5. e. Find the probability density function f(x). 1. Define 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 x)) is given to be: F(x) { 0 < 0 exp(-0.03x1.2) = 1 e0.03x1.2 x > 0 a. What is the probability that a jet engine will last less than 12 months before needing to be rebuilt? rior Sev b. What is the probability that a jet engine will last more than 12 months before needing to be rebuilt? c. 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? d. Find the 50-th percentile of X. That is to say the value of x such that P(X x) = 0.5. e. Find the probability density function f(x).