A system for a random amount of time X (in units of months) is given by a density/2xe; x>0,; x<0.f(x) =Find the moment generating function of X. Hence, compute the variance ofX.(a)(b)Deduce the expression for the k th moment.Obtain the distribution function of X. Hence, compute that the probabilitythat, 7 of such system, at least 4 will function for at least 6 units of months.State the assumptions that you make.(c)

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Answered: A system for a random amount of time X…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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