# Math Help - What's a gamma distribution and how does one apply an mgf to it?

1. ## What's a gamma distribution and how does one apply an mgf to it?

Apply the m.g.f. of the gamma distribution to find its expectation and variance. Any help will be very much appreciated thank you so much.

2. Do you mean OBTAIN the mgf of a gamma?
That's been done here before.
Just combine the exponential terms and observe the new beta (so it's a valid density)
and you're done.

3. Well, if you are given the mgf, M(t), then
$E[X]=\frac{d}{dt}M(0)$
and
$Var(X)=E[X^2]-(E[X])^2=\frac{d^2}{dt^2}M(0)-(E[X])^2$

If you are not given the mgf, then you have to calculate
$M(t)=\int_{- \infty}^{\infty}e^{tx}f(x)dx$ where f(x) is the pdf of the gamma distribution