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# Thread: Deriving MGF for exponential

1. ## Deriving MGF for exponential

I understand that M(t) = E[e^tX]

so for example, for exponential with mean 1/c would be

integral (0, inf) e^tx * ce^-cx dx

which simplifies to

c * integral (0, inf) e^x(t-c) dx

but how do we know whether (t-c) < 0 or not?

2. If t >= c, then the integral may be INF, and that means the MGF is not exist.
And when t < c, the MGF exists and it equal to c/(c-t).

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