7.7.3 Let X₁,..., Xn be a set of independent random variables with a U(0, 8) distribution, and letT = max (X₁,..., Xn)(a) Explain why the cumulative distribution function of T'isF(t) = (-)"for 0 ≤(b) Show that the probability density function of Tisf(t) = (;)"foro < t < 0.4(c) Show thatÂ="HTis an unbiased point estimate of 0) What is the standard error of(e) Suppose that n = 10 and that the following data values are obtained:1.26.37.36.43.50.24What are the values of ? and the standard error of ô?4.67.1 5.01.8

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Answered: 7.7.3 Let X₁, Xn be a set of…

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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Suppose that a study of a certain computer system reveals that the response time, in seconds, has an exponential distribution with density curve f(x) = (1/3)e(-x/3) for x > 0 and f(x) = 0 otherwise. What is the probability that response time exceeds 5 seconds? What is the probability that response time exceeds 10 seconds?
If the random variable T is the time to failure of a commercial product and the values of its probability den-sity and distribution function at time t are f(t) and F(t), then its failure rate at time t is given by f(t)1 − F(t). Thus, thefailure rate at time t is the probability density of failure attime t given that failure does not occur prior to time t.(a) Show that if T has an exponential distribution, thefailure rate is constant. (b) Show that if T has a Weibull distribution (see Exer-cise 23), the failure rate is given by αβt β−1.
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