Customers arrive at a facility according to a Poisson process N(t) of rate λ = 4.5 customers/hour. Each customer isadmitted to the facility with probability p = 0.8. All customers, who are not admitted, leave and do not come back. LetX(t) be the number of customers admitted from time 0 to time t. Compute the following:(a) The mean value E[X(6.5)] = 23.4(b) The probability P(X(6.5) = 23) ==(c) The conditional probability P(X(6.5) = 23 | N(6.5) = 30) =%.%.Note: For parts (b) and (c), enter your answers as percentages but do not type the percent sign.

Concept used here:In a Poisson process, the number of events occurring in a fixed period of time or…

Answered: Customers arrive at a facility…

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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The inhabitants of a city develop skin cancer at an approximate rate X. For those people who have developed skin cancer, some proportion p E (0, 1) will die from the disease. Assume a simple model such that n, the number of people who develop skin cancer, is distributed Poisson(A). Let X denote the people who die from skin cancer in this city. Then, assuming that every cancer patient is independent of the others, and that the proportion p is constant: ~ U Poisson(A) X\n - Binomial(n, p) Question 4: What is the marginal distribution of X? Hint: two primary ways to do this: 1. you can summate out n from the joint distribution directly (more straightforward, but tricky algebra) o Pay attention to the lower limit of n o Remember that i=0 2. use MGFS + iterated expectation: E[etx] = En|Exn[etx n|| and then recognize the distribution corresponding to the MGF (need to understand MGFS and iterated expectation). o Obtain the inner expectation by using the Binomial theorem. O X Binoтial(n, Ap)…

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