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 does the joint pdf represent in probability theory?
💡 Hint: Think about how two random variables can interact.
Question 2
Easy
What is the integral used for when finding marginal distributions?
💡 Hint: Recall the definition of marginalization.
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 does the marginal distribution of a variable express?
- The distribution of the entire population
- The distribution of a single variable
- ignoring others
- Only the joint probability
- The probability distribution over a range of data
💡 Hint: Think of how we analyze one aspect at a time.
Question 2
True or False: You can always reconstruct joint pdfs from marginal distributions if the variables are dependent.
- True
- False
💡 Hint: Consider the definition of dependency.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Consider the joint pdf f(x,y) = 4x^2y^2 for 0 < x < 1, 0 < y < 1. Derive both marginal distributions.
💡 Hint: Remember to integrate over the other variable to calculate each marginal.
Question 2
Given a joint pdf f(x,y) = xy for 0 < x < 2 and 0 < y < 2, analyze its marginal distributions and check if the variables are independent.
💡 Hint: Revisit the definition of independence and how it applies to our findings.
Challenge and get performance evaluation