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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the marginal PMF of X for the discrete distribution given?
💡 Hint: Sum the probabilities where X equals 0.
Question 2
Easy
How can you check if two random variables X and Y are independent?
💡 Hint: Use the joint PMF for verification.
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 joint probability mass function define?
- Probability of single outcomes
- Probability for pairs of random variables
- Probability for mixtures
💡 Hint: Think about how they relate to each other.
Question 2
True or False: Marginal distributions can always be derived from joint distributions.
- True
- False
💡 Hint: Recall the method of finding marginals.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Consider a random variable Z defined with a joint PMF across three dimensions. Determine the marginal PMF for Z and check if it influences the independence of the two other dimensions.
💡 Hint: Break the problem down dimension by dimension!
Question 2
Given a continuous distribution defined in a non-standard region, derive its joint PDF and confirm its validity before calculating marginal PDFs.
💡 Hint: Focus on region boundaries for proper limits!
Challenge and get performance evaluation