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N(t) A compound Poisson process X is given by X(t) = Y n , where {N(t);t 0} is a Poisson process with rate and n=1

N(t)

A compound Poisson process X is given by X(t) = Yn , where {N(t);t 0} is a Poisson process with rate and

n=1

Y1, Y2, are i.i.d. random variables. Write for the moment generating function of Y1. Show that the moment generating function of X(t) has a solution expressible in (, t, ).

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