hi, i need help with this one,
by using Moment-generating function, show that :
thanks to all!
Hello,
$\displaystyle \chi^2_n$ has the MGF $\displaystyle G(t)=\frac{1}{\sqrt{(1-2t)^n}}=\frac{1}{(1-2t)^{n/2}}$
$\displaystyle \Gamma(n,\lambda)$ has the MGF $\displaystyle G(t)=\left(\frac{\lambda}{\lambda-t}\right)^n$
so $\displaystyle \Gamma(n/2,1/2)$ has the MGF $\displaystyle G(t)=\left(\frac{1/2}{1/2-t}\right)^{n/2}=\left(\frac{1}{1-2t}\right)^{n/2}$
and this is the same as above
There's sometimes a problem, as to know whether the second parameter of the Gamma distribution is $\displaystyle \theta$ or $\displaystyle \frac 1 \theta$
From the book I have, it said that the MGF is like I wrote above.
So now it depends on how your teacher usually defines the second parameter.