1. Suppose events occur in time according to a Poisson Process with rate 1 per minute.(a) State the distribution of X, the number of events occuring in a one-hour time period, andhence show that the probability that no events occur in this one-hour time period is e-601.(b) The process starts at time 0. Let the time to the first event be Y minutes. State thedistribution of Y and hence, or otherwise, find the probability that the first event occursafter 60 minutes.(c) The kth event (k 2 2) occurs at time Z minutes. Explain clearly how the following result canbe used in the context of this Poisson Process to confirm that Z has a gamma distribution.State the parameters of this distribution.Result: if X, X2,...,X, are independent exponential random variables each with mean u,then E-1 Xi Gamma(n, u).

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Answered: 1. Suppose events occur in time…

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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