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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define joint distribution and provide examples of its types.
💡 Hint: Think about how we measure joint occurrences.
Question 2
Easy
State the formula for joint PMF.
💡 Hint: Look at how we express probabilities for discrete cases.
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 a joint distribution describe?
- The distribution of a single variable
- The relationship between two or more variables
- The probability of a variable over time
💡 Hint: Think about what relationships we study in statistics.
Question 2
True or False: Two independent random variables must have a joint distribution that equals the product of their marginal distributions.
- True
- False
💡 Hint: Recall the independence formula discussed in class.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Consider a joint PMF table for random variables X and Y:
| Y/X | 1 | 2 |
|---|---|---|
| 1 | 0.2 | 0.3 |
| 2 | 0.1 | 0.4 |
Check the independence of X and Y.
💡 Hint: Look for any discrepancies between the joint PMF and the products of marginals.
Question 2
Given f(x,y) = xe^{-x}ye^{-y} for x,y>0, determine if X and Y are independent.
💡 Hint: Verify by directly calculating the products of the marginals!
Challenge and get performance evaluation