<< Statistics`ContinuousDistributions`
num := ν
den := η
fdist := FRatioDistribution[num, den]
\(	"Función de densidad"\)
stpdf = PDF[fdist, x]
\(	"Función característica"\)
f[t_] = CharacteristicFunction[fdist, t]
\(	"Primer momento"\)
AA = (1/I)*f'[
          0]

\(	"Segundo momento"\)
BB = (1/(I^2))*f''[0]
Simplify[(BB) - 
        2 (AA) (AA) + (((AA))^2)]

\(	"Tercer momento"\)
CC = (1/(I^3))*f'''[0]
Simplify[(CC) - 3 (BB) (AA) + 
        3 (AA) (((AA))^2) - (((AA))^3)]

\(	"Cuarto momento"\)
DD = (1/(I^4))*f''''[0]
Simplify[(DD) - 4 (CC) (AA) + 6 (BB) (((AA))^2) - 
        4 (AA) (((AA))^3) + (((AA))^4)]

Simplify[(((η^2) (1 + (ν/2)))/(2 (1 - (η/2)) (2 - (η/2)) ν)) - (((-(η/(2 (1 - (η/2))))))^2)]

Simplify[% - (2 ((((η/(η - 2))))^2) (((η + ν - 2)/((η - 4) ν))))]