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Math Help - Conditional Expectation of Poisson Processes

  1. #1
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    Conditional Expectation of Poisson Processes

    Suppose that Xt is a Poisson Process with parameter λ = 1. Find E(X1 | X2) and E(X2 | X1).

    I think they should be equal but I'm not sure how to write the value of the expectation of either.
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  2. #2
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    Re: Conditional Expectation of Poisson Processes

    Hey bjnovak.

    Can you calculate the conditional distribution for P(X1=x|X2=y) and find its expectation?

    You also have to tell us what kind of expectation you want to find since it is a multi-dimensional random variable: the expectation can be any general function of X1 and X2 or E[f(X1,X2)] and if you don't specify this then it won't make sense.
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  3. #3
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    Re: Conditional Expectation of Poisson Processes

    I believe the expectation is E[f(X1,X2)] where E( X2 | X1) (x) = f(X1,X2) is the (sum over X2 of X2*f(X1,X2) )
    / f over X1 (X1) (equation from book).

    I'm not sure how the poisson process applies to this
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  4. #4
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    Re: Conditional Expectation of Poisson Processes

    That means that in this particular case f(X1,X2) = X2.

    If you find the conditional distribution and get E[X2] of that distribution (it will be bivariate) then you can show what you need to show.
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