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Homework Help: Poisson arrivals and mgf

  1. Sep 4, 2010 #1
    1. The problem statement, all variables and given/known data

    Suppose cars arriving at an intersection follow a poisson distribution and that the number of passengers in the nth car is Yn where n>=1 and they are iid and independent of Nt each with moment generating function My(k)

    Write Zt as a sum of iid random variables and show:

    mgf of Zt = exp[ lambda*t*(My(k)-1)]

    3. The attempt at a solution

    Probability of Yn passengers in the nth car is P(Yn) * P(Nt)

    (1/n) * [exp(-labmda*t) *(lambda*t)^n] / n!

    If I calculate the mgf from here it doesnt lead to the correct answer.

    How is Zt written as a sum of iid random variables from this?
    Thanks in advance for any help
     
  2. jcsd
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