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3 cards from this section. Quick, good the night before a test.
What is the definition of a moment generating function?
Think about how moments relate to expected values.
What does the first derivative of an MGF evaluated at zero represent?
Consider what the mean describes in a distribution.
What is the main use of a moment generating function?
Think about the summary aspect of probability distributions.
True or False: The second moment of a distribution is always the variance.
Remember the formula for variance.
Given a random variable with MGF M(t) = (1 - 2t)^-3, find the mean and variance.
Use the properties of the derivatives of MGFs to find moments.
Design an MGF for a random variable that has a mean of 5 and variance of 2.
Consider how you can use the mean and variance to shape the MGF.
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