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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the mathematical condition for independence between two discrete random variables?
💡 Hint: Look at the relationship between joint and marginal probabilities.
Question 2
Easy
How do we express independence in continuous random variables?
💡 Hint: Focus on how we relate joint PDF to marginal PDFs.
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
Which of the following is TRUE for independent random variables?
- P(X
- Y) = P(X) + P(Y)
- P(X
- Y) = P(X) * P(Y)
- f(x
- y) = f(x) + f(y)
💡 Hint: Think about what independence mathematically implies.
Question 2
True or False: If two random variables are independent, their covariance is always zero.
- True
- False
💡 Hint: Consider how correlation and independence relate.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A joint PMF of two discrete variables X and Y is provided. Calculate the marginal distributions and test if X and Y are independent. If X has values 1, 2 with corresponding probabilities, and Y has values 3, 4, write out the joint PMF table.
💡 Hint: Don't forget to sum across both variables carefully.
Question 2
Given a continuous joint PDF f(x, y) = xy for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1, derive the individual PDFs and check independence.
💡 Hint: Set up correct limits for integration and pay attention to normalization.
Challenge and get performance evaluation