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Math Help - Poisson processes

  1. #1
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    Poisson processes

    Hi,

    Next time I promise I won't learn a new chapter just the day before the exam

    We have two Poisson processes N_1(t) and N_2(t) which are independent (with parameters \lambda,\mu)

    Then N(t)=N_1(t)+N_2(t) is a Poisson process with parameter \lambda+\mu. Okay with that.

    And it follows (how ??) that N_2(t)-N_1(t) have the same distribution as \sum_{i=1}^{N(t)} \epsilon_i, where P(\epsilon_i=1)=\frac{\lambda}{\lambda+\mu} and P(\epsilon_i=-1)=\frac{\mu}{\lambda+\mu}

    I don't understand at all where the last part comes from

    Thanks for any help
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  2. #2
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    If you got how the step came, please post it. I have my Random process exam tom, it will be really helpful.

    Thanks in advance
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