(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose that passengers arrive at a train terminal according to a poisson process with rate "$". The train dispatches at a time t. Find the expected sum of the waiting times of all those that enter the train.

2. Relevant equations

F[X(t+s)-X(s)=n]=((($t)^n)/n!)e^(-$t))

It is the equation of Poisson Processes.

3. The attempt at a solution

The waiting time for every person is unique, since he arrives at a different time. So, the sum of the waiting time will have a certain value. However, I am unable to understand how can the sum have an "expected value". I mean, what parameters is the sum depending on? I can only see time as a variable here. Ofcourse, the other variable is the number of people arriving, but once that is set up, shouldnt the sum be unique?

Can you help me out in setting up the problem? I am sure that If I am given a setup and equations, I can arry out the solutions myself.

Thank you.

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# Stochastic Processes, Poisson Process | Expected value of a sum of functions.

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