Question

Given MX(t) = 0.2 + 0.3e^t + 0.5e^3t, find
(a) the PMF pX(x) (no justication required).
(b) the expected value E[X^n] for n = 1, 2, 3......[Find a general formula.]

Answer 1

a) The moment generating function for any random variable X is defined as:

As, we are given here that:

Therefore, the PMF for X here is given as:
P(X = 0) = 0.2,
P(X = 1) = 0.3,
P(X = 3) = 0.5

This is the required PMF here.

b) The n^th moment of X here is computed as:

This is the required general formula for the n^th moment of X here.