Q3 Let N(t) be the number of failures of a computer system on the interval [0, t]. We supposethat {N(t), t >0} is a Poisson process with rat A = 1 per week.Q3(i.) Calculate the probability that the system functions without failure during two consecutiveweeks.Q3 (ii.) Calculate the probability that the system has exactly two failures during a given week,knowing it has functioned without failure during the previous two weeks.Q3 (iii.) Calculate the probability that less than two weeks elapse before the third failure occurs.Q3 (iv.) LetZ(t) = e-Ne), for t>0.Show thatE[Z(t]] = exp{t(e¬l – 1)]using conditioning arguments.

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Answered: Q3 Let N (t) be the number of failures…

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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