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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the joint probability density function (pdf)?
π‘ Hint: Think about how two random events relate.
Question 2
Easy
Define marginal distribution.
π‘ Hint: What do we focus on when we 'marginalize'?
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 a marginal distribution?
- A function for two variables
- Distribution of one variable
- Sum of joint probabilities
π‘ Hint: Think about the process of simplifying.
Question 2
True or False: Marginal distributions can reconstruct joint distributions.
- True
- False
π‘ Hint: Consider independence in your reasoning.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the joint pdf π(π₯,π¦) = 12π₯π¦ for 0 < π₯ < 1 and 0 < π¦ < 1, calculate the marginal distributions of π and π.
π‘ Hint: Focus on integrating each variable's contribution.
Question 2
Discuss the independence condition for two random variables and provide an example illustrating this with marginal pdfs.
π‘ Hint: Consider if separating their probabilities affects their joint behavior.
Challenge and get performance evaluation