Worked Example

Example 8: MGF from PMF Table

Table to MGF

Given a discrete random variable X with f(x) as follows: \\[0.5em] \begin{array}{c|ccccc} x & 0 & 1 & 2 & 3 & 4 \\ \hline f(x) & 0.1 & 0.2 & 0.4 & 0.2 & 0.1 \end{array} \\[0.5em] (a) Find the moment generating function of X, M_X(t). \\[0.5em] (b) Use the M_X(t) obtained in (a) to calculate: (i) E(X), (ii) V(X).

Solution

Step 1 of 3

Step 1

(a) Find M_X(t) = Σe^{tx}·f(x) for all x

Sum e^(tx)·f(x) for x = 0, 1, 2, 3, 4

info

Perfect! Applied MGF definition M_X(t) = Σe^{tx}·f(x).