Calls arrive at a switchboard as a Poisson process with rate λ = 4 per minute. Find the probabilities that, with respect to any fixed origin in time, the twelfth subsequent call arrives: (a) before two minutes have elapsed [hint: consider the distribution of the number of calls arriving in these two minutes], (b) after three minutes and before five minutes have elapsed.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Stochastic process, Poisson process. 

Calls arrive at a switchboard as a Poisson process with rate λ = 4 per minute. Find
the probabilities that, with respect to any fixed origin in time, the twelfth subsequent
call arrives:
(a) before two minutes have elapsed [hint: consider the distribution of the number
of calls arriving in these two minutes],
(b) after three minutes and before five minutes have elapsed.
Transcribed Image Text:Calls arrive at a switchboard as a Poisson process with rate λ = 4 per minute. Find the probabilities that, with respect to any fixed origin in time, the twelfth subsequent call arrives: (a) before two minutes have elapsed [hint: consider the distribution of the number of calls arriving in these two minutes], (b) after three minutes and before five minutes have elapsed.
Expert Solution
Step 1

Given

             λ=4 per minute

Now

             X~Exp(λ)

that is

            X~Exp(4)

As we know that

            P(x<X)=1-e-λx

and      P(x>X)=e-λx

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