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Question about probability and poisson process

  1. Mar 31, 2009 #1
    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!
     
  2. jcsd
  3. Mar 31, 2009 #2
    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.
     
  4. Mar 31, 2009 #3
    Thank you. As your suggestion, I found the solution.
     
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