Question about probability and poisson process

  • Thread starter quacam09
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Hi all, I have a question about probability. Can you help me?

There are 2 events:
- Customer A arrives the system B in accordance with a Poisson process with rate Lambda1
- Customer A arrives the system C in accordance with a Poisson process with rate Lambda2.

Given that Poisson processes are mutually independent. Computing the probability of the event that customer A arrivers the system B and the probability of the event that customer A arrivers the system C?

Thank you!
 
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1
I'm guessing there is only one custumer. The holding times are exponential with parameter lambda. The question then is [itex]\mathbb{P}(\mathbf{e}_{\lambda_1}< \mathbf{e}_{\lambda_2})[/itex]. Condition on one of them and use the law of total probability.
 
Thank you. As your suggestion, I found the solution.
 

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