$E(F)=int xf_{k,m}dx$ where $f_{k,m}(t) = Gamma(t)=frac{Gamma((k+m)/2)}{Gamma (k/2)Gamma(m/2)}k^{k/2}m^{m/2}t^{k/2 – 1}(m+kt)^{-(k+m)/2}$.
How do you find $E(F)$? Say you have to convert $x*f(k,m)$ to $C * f(k’,m’)$ where $f(k’,m’)$ is a pdf itself, which leaves $E(F)=C$ (which is$frac{m}{m-2}$).
