Worked Example

Example 7: MGF for Discrete Values

Simple MGF

Suppose that X is a random variable that has the probability function: \\[0.5em] f(x) = \begin{cases} 0.5, & x = 6 \\ 0.3, & x = 8 \\ 0.2, & x = 10 \end{cases} \\[0.5em] (a) Find the moment generating function for X. \\[0.5em] (b) Using part (a), find E(X) and V(X).

Solution

Step 1 of 5

Step 1

(a) Find the moment generating function M_X(t) = E(e^{tX}) = Σe^{tx}·f(x)

Sum e^(tx)·f(x) for x = 6, 8, 10

info

Perfect! Applied the MGF definition for discrete variables.