Practice Definition (11.3.1) - Moments and Moment Generating Functions

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6 sample questions

Question 1.
Define a Moment Generating Function.
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Think about how functions can capture properties of distributions.
Question 2.
What is the first moment obtained from an MGF?
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Consider the relationship to the expectation operator.
3Question 3.
What is the MGF of a random variable X?
- E[X]
- E[e^{tX}]
- E[X^2]
- E[X+Y]
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Remember the functional form used for MGFs.
4Question 4.
True or False: The MGF uniquely determines the distribution of a random variable.
- True
- False
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Think about the implications of having the same MGF.
Question 5.
A random variable X has an MGF M_X(t) = e^{(3 + t)/2}. Find the mean and variance of X.
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Start with derivative calculations for moments.
Question 6.
For two independent random variables X and Y with known MGFs, compute the MGF for Z = X + Y.
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Don't forget the independence property while calculating.

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