Exponential distribution moment generating function to find the mean

[Askhwhelp]

With mean = 2 with exponential distribution

Calculate

E(200 + 5Y^2 + 4Y^3) = 432

E(200) = 200

E(5Y^2) = 5E(Y^2) = 5(8) = 40

E(4Y^3) = 4E(Y^3) = 4(48) = 192

E(Y^2) = V(Y) + [E(Y)]^2 = 2^2+2^2= 8

E(Y^3) = m_Y^3(0) = 48(1-2(0))^{-4} = 48

is this right?

 

[Askhwhelp]

Please take a look of this