What is the probability 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? 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?

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a. What is the probability 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?


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?

4. Define the continuous 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 (note
this is the cumulative distribution function F(x), not the density function f(x)):
F(x) = P(X ≤ x) =
0
{:
1 — exp (-0.03x¹.2) = 1 – 6
-0.03x
1.2
x ≤ 0
0 < x <∞
Transcribed Image Text:4. Define the continuous 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 (note this is the cumulative distribution function F(x), not the density function f(x)): F(x) = P(X ≤ x) = 0 {: 1 — exp (-0.03x¹.2) = 1 – 6 -0.03x 1.2 x ≤ 0 0 < x <∞
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