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? 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).
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? 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).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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) \((P(X \leq x))\) is given to be:
\[
F(x) =
\begin{cases}
0 & x \leq 0 \\
1 - \exp\left(-0.03x^{1.2}\right) = 1 - e^{-0.03x^{1.2}} & x > 0
\end{cases}
\]
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?
d. Find the 50-th percentile of X. That is to say the value of x such that \(P(X \le x) = 0.5\).
e. Find the probability density function f(x).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff2db349d-44e2-4dc0-ad50-be44fa6802da%2F767df3c0-c640-4ab1-97ef-19bab39e90da%2Fejggjsb_processed.png&w=3840&q=75)
Transcribed Image Text: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) \((P(X \leq x))\) is given to be:
\[
F(x) =
\begin{cases}
0 & x \leq 0 \\
1 - \exp\left(-0.03x^{1.2}\right) = 1 - e^{-0.03x^{1.2}} & x > 0
\end{cases}
\]
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?
d. Find the 50-th percentile of X. That is to say the value of x such that \(P(X \le x) = 0.5\).
e. Find the probability density function f(x).
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