Poisson process problem

  1. Given a poisson process Z(t) with a given rate lamda, k and m nonnegative integers and t and c real and positive numbers, calculate the probability:
    P(Z(t-c)=m | Z(t)=k)

    thanks
     
  2. jcsd
  3. Hint: conditional on the number of jumps in a Poisson process, the jump times are uniformly distributed over the time interval.
     
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