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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Answered: a. What is the probability that a jet…

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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Listed below, from left to right and then top to bottom, are numbers of law enforcement fatalities for 20 recent and consecutive years. First find the mean, identify each value as being above the mean (A) or below the mean (B), then test for randomness above and below the mean using α = 0.05. Is there a trend? 183 140 173 172 144 163 242 159 150 165 164 155 191 147 124 160 171 125 106 116 The mean is. (Type an integer or a decimal. Do not round.) C
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In a Normal distribution, the Empirical Rule states that... ["", "", "", "", ""] of the data is within 1 standard deviation of the mean, ["", "", "", "", ""] of the data is within 2 standard deviation of the mean, and ["", "", "", "", ""] of the data is within 3 standard deviation of the mean.
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