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2 cards from this section. Quick, good the night before a test.
What is the formula for the moment generating function of a random variable X?
Think about expectations and exponentials.
True or False: If two random variables are independent, their MGFs can be added.
Focus on the properties of MGFs.
What does the moment generating function M_X(t) represent?
Think about what MGFs do in relation to random variables.
True or False: The first moment can be derived from the first derivative of the MGF.
Remember how derivatives relate to moments.
A discrete random variable has an MGF of M_X(t) = (0.5 * e^t + 0.5 * e^2t). Calculate the first two moments using this MGF.
Differentiate MGF twice, evaluate at t=0.
Given two independent random variables with MGFs M_X(t) = e^(2t) and M_Y(t) = e^(3t), find M_{X+Y}(t).
Use the property of additivity of MGFs.
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