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Please be sure to answer the questionProvide details and share your research!If X and Y are independent, then E(es(XY )) = E(esXesY) = E(esX)E(esY), and we conclude that the mgf of an independent sum is the product of the individual mgf's Sometimes to stress the particular rv X, we write M X(s) Then the above independence property can be concisely expressed as MIf f ;g functions on Rn, formally define (f g)(x) = Z f(x y)g(y)dy Theorem Suppose that f ;g 2L1(Rn) Then for almost all x, the function f(x y)g(y) is integrable in y, and Z (f g)(x) dx kfk L1 kgk L1 Hart Smith Math 526
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