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Moment generating function help?

by millwallcrazy
Tags: function, generating, moment
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millwallcrazy
#1
May11-10, 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/(t-A) if that helps

Thanks
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statdad
#2
May12-10, 08:06 AM
HW Helper
P: 1,372
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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