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

I cannot figure out this example:

suppose that initially individuals enter a room from one door according to a Poisson process with arrival rate lambda1. Suppose that as soon as one inidividual enters, this door is shut down and a second door is open. The numer of individuals that enter the room from the second door follows a Poisson process with arrival rate lambda2. As soon as a second inidividual enters the room, the second door is shut down and a third door is opened; from that one the number of individuals entering from that door follows a posson with rate lambda3. and so on...

what is probability that at time t I have exactly n individuals? THANKS!

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Poisson process with different arrival rates

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