Practice Moment Generating Functions (mgfs) (11.3) - Moments and Moment Generating Functions

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6 sample questions

Question 1.
What is the definition of a Moment Generating Function?
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Think about the expected value.
Question 2.
List the property that allows obtaining the r-th moment from an MGF.
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Consider how derivatives work.
3Question 3.
What is the calculation for the first moment using an MGF?
- M_X(0)
- M'_X(0)
- E[X^2]
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Consider what derivation reveals about the function.
4Question 4.
True or False: MGFs can be used for dependent random variables.
- True
- False
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Reflect on how independence affects calculations.
Question 5.
If X ~ N(0,1) has an MGF given by M_X(t) = exp(t^2/2), derive E[X^2] and variance.
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Differentiate the MGF to find moments.
Question 6.
Consider a random variable with probabilities P(X=1)=1/3, P(X=2)=2/3. Find the MGF, first moment, and variance.
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Make sure to differentiate and evaluate properly.

4 more questions in this section. Enroll free to practise them all.