schoolUiTM MOOC/Mathematical Statistics 1/Topic 1 Part 3/Example 7: MGF for Discrete Values

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Example 7: MGF for Discrete Values

Simple MGF

Problem Statement:

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).

Proof Execution TraceSTEP 1 / 5

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Step 1Choose One

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

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Quick Reference

Formulas and theorems from Topic 1