Question: 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) = Y_n, 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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