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Calculating covariance

  1. Jun 22, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the Cov(X(t), X(t+s)) where X(t) = N(t+1)-N(t), where N(t) is a poisson process with parameter [tex]\lambda[/tex].

    2. Relevant equations

    3. The attempt at a solution
    X(t) should be poisson distributed with mean [tex]1\lambda[/tex] by stationary increments, and X(t+s) should be poisson distributed with mean [tex]\lambda[/tex]. This reduces to finding the covariance of 2 dependent poisson([tex]\lambda[/tex]) random variables (since X(t) and X(t+s) is dependent, so the answer isn't just = variance = [tex]\lambda[/tex]). Now what do I do?
  2. jcsd
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