Recall that the gamma function is defined asr(r) =T"-le¬"dxfor r > 0. You can use without proof that I'(r + 1) = r[(r) for r > 0 in this problem.Let v be a positive real number and X be a random variable with probability density'e if r >0fx(x) =otherwise.(a)Let Y = 1/X. Specify the distribution of Y including parameters.(b)Find E[Y].

Answered: Image /qna-images/answer/71f2a429-83e6-4984-8aa7-2d09a7b225b0.jpg

Answered: (a) Let Y = 1/X. Specify the…

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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Find the z-scores for which 28% of the distribution's area lies between −z and z.
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Find the characteristic function of X² when X has the N(u, o²) distribution.
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"Time headway" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X = the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow. The pdf of X is the following. 0.17e-0.17(x - 0.5) - {0.17e-0.1 x ≥ 0.5 otherwise (a) What is the probability that time headway is at most 6 sec? (Round your answer to three decimal places.) f(x) = (b) What is the probability that time headway is more than 6 sec? At least 6 sec? (Round your answers to three decimal places.) more than 6 sec at least 6 sec (c) What is the probability that time headway is between 5 and 6 sec? (Round your answer to three decimal places.)

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(a) Let Y = 1/X. Specify the distribution of Y including parameters. (b) Find E[Y].