<<Statistics`DiscreteDistributions`
media := μ

disgeo := GeometricDistribution[media]

pdfb1 = 
      PDF[disgeo, x]
f[t_] = 
      CharacteristicFunction[disgeo, t]
"First raw moment = first central moment"
AA = (1/I)*f'[0]

"Second raw moment"
BB = (1/I^2)*f''[0]
Simplify[(BB) - 2 (AA) (AA) + (((AA))^2)]

"Third raw moment"
CC = (1/I^3)*f'''[0]
Simplify[(CC) - 3 (BB) (AA) + 
          3 (AA) (((AA))^2) - (((AA))^3)]

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