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2 cards from this section. Quick, good the night before a test.
Define a raw moment.
Think of moments calculated about the origin.
What does the first central moment measure?
Consider how deviations from the mean behave.
What is the first central moment?
Think about the definition of deviation from the mean.
If MGFs exist for random variables, they uniquely determine their distributions.
Remember what MGFs do for distributions.
Given a discrete random variable with a specific distribution, compute its first four moments using the definitions.
Use the definition of moments learned earlier.
Show how MGFs can simplify finding variances for two independent random variables.
Remember the additivity property of MGFs!
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