11.3.1 - Definition
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Practice Questions
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Define a Moment Generating Function.
💡 Hint: Think about how functions can capture properties of distributions.
What is the first moment obtained from an MGF?
💡 Hint: Consider the relationship to the expectation operator.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the MGF of a random variable X?
💡 Hint: Remember the functional form used for MGFs.
True or False: The MGF uniquely determines the distribution of a random variable.
💡 Hint: Think about the implications of having the same MGF.
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Challenge Problems
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A random variable X has an MGF M_X(t) = e^{(3 + t)/2}. Find the mean and variance of X.
💡 Hint: Start with derivative calculations for moments.
For two independent random variables X and Y with known MGFs, compute the MGF for Z = X + Y.
💡 Hint: Don't forget the independence property while calculating.
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