# moment generating function help?

by millwallcrazy
Tags: function, generating, moment
 P: 14 I know that hte MGF is = the E[e^tx] How do i show that if i take a sample (X1;X2; : : :Xn) from the exponential density f(x) = A*e^(-Ax), then the sum Z = sum(Xi) has the gamma density? I found that the MGF for the exponential was A/(t-A) if that helps Thanks
 HW Helper P: 1,344 Note that $$e^{t\sum X_i}} = \prod{e^{tX_i}}$$ This will relate the form of the mgf of the sum to the individual mgfs of the sample.

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