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Moment generating function help? 
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#1
May1110, 01:12 PM

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/(tA) if that helps Thanks 


#2
May1210, 08:06 AM

HW Helper
P: 1,361

Note that
[tex] e^{t\sum X_i}} = \prod{e^{tX_i}} [/tex] This will relate the form of the mgf of the sum to the individual mgfs of the sample. 


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