moments and moment generating functions

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Last updated 11:58 PM on 4/21/26
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5 Terms

1
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Moment Generating Function (MGF)

A function defined as MX(t)=E[etX]M_X(t) = E[e^{tX}] that encodes all moments of a random variable.

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Expectation (E)

The average value of a random variable, used in the definition of the Moment Generating Function.

3
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Sum of Independent Random Variables

The Moment Generating Function is useful for finding the distribution of this type of sum.

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What is the definition of Moment Generating Function (MGF)?

MX(t)=E[etX]M_X(t) = E[e^{tX}], which encodes all moments of a random variable.

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What does the Moment Generating Function encode?

All moments of a random variable.