Question

Let Z be the random variable with support SZ = {1,2,3} and pmf f(z) = z/6, for z ∈ SZ .

(a)  Find the MGF (moment generating function) of Z, Mz(t).

(b) Using Mz(t), calculate E[z^3].

Answer 1

Solution :

We have the pmf of a random variable Z as follows :

f(z) = z/6 ; z ∈ {1, 2, 3}

a) The MGF of a discrete random variable Z is given as follows :

b) E(Z³) is given as follows :