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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What does it mean for random variables to be independent?
💡 Hint: Think of the dice examples we discussed.
Question 2
Easy
How is the joint PMF represented for discrete random variables?
💡 Hint: Refer to the table format presented in our example.
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 indicates that two random variables are independent?
- P(X,Y) = P(X) * P(Y)
- P(X,Y) < P(X) * P(Y)
- P(X,Y) > P(X) * P(Y)
💡 Hint: Anchor this to the conditional probabilities we discussed.
Question 2
In discrete random variables, which function describes the joint probabilities?
- Marginal Probability Function
- Joint Probability Mass Function
- Mutual Information
💡 Hint: Check the terminology we used before.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given X and Y with the joint PDF f(x,y) = e^(-x) * e^(-y), derive whether X and Y are independent.
💡 Hint: Calculate the marginal PDFs first.
Question 2
Create a joint PMF for X and Y that showcases independence and calculate all relevant probabilities.
💡 Hint: Make sure distributions sum to 1 and check independence condition afterward.
Challenge and get performance evaluation