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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the definition of a Moment Generating Function?
💡 Hint: Think about the expected value.
Question 2
Easy
List the property that allows obtaining the r-th moment from an MGF.
💡 Hint: Consider how derivatives work.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the calculation for the first moment using an MGF?
- M_X(0)
- M'_X(0)
- E[X^2]
💡 Hint: Consider what derivation reveals about the function.
Question 2
True or False: MGFs can be used for dependent random variables.
- True
- False
💡 Hint: Reflect on how independence affects calculations.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
If X ~ N(0,1) has an MGF given by M_X(t) = exp(t^2/2), derive E[X^2] and variance.
💡 Hint: Differentiate the MGF to find moments.
Question 2
Consider a random variable with probabilities P(X=1)=1/3, P(X=2)=2/3. Find the MGF, first moment, and variance.
💡 Hint: Make sure to differentiate and evaluate properly.
Challenge and get performance evaluation