Suppose X₁, X2,... are i.i.d. with moment generating function Mx(t). Let N be a nonnegative integer-valued random variable, independent of the X;, with moment generating function My(t). Consider the random sum S ₁X₁. In terms of Mx and My, find the moment generating function of S. Use this to rederive the mean of S. Specializing to the case where the Xį are Poisson with mean λ and N is Poisson with mean fly what is the moment generating function of S? =

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