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    mean of 2 Poisson process variables




    I have a Poisson process N(t)~Poiss(t*lambda), what is the mean of E(N(6)*N(10))
    because it is a a Poisson process N(6) and N(10) are dependent (i think )

    I have tried using law of total expectation and co-variance without any success.

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    Re: mean of 2 Poisson process variables

    N(6) and N(10) are dependent
    How about N(6) and N(10) - N(6)?

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    Re: mean of 2 Poisson process variables

    Quote Originally Posted by BGM View Post
    How about N(6) and N(10) - N(6)?
    Keeping in mind that N(10) = [N(10) - N(6)] + N(6)
    I don't have emotions and sometimes that makes me very sad.

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    Re: mean of 2 Poisson process variables

    is it right to say that N(10) - N(6)=N(4) because
    N(10) - N(6)={the amount of appearances between time 6 and 10}=N(4)

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    Re: mean of 2 Poisson process variables


    It isn't N(4) but is has the same distribution as N(4)
    I don't have emotions and sometimes that makes me very sad.

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