Professional Courses
Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Categories
Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
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