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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What does it mean for two random variables to be independent?
💡 Hint: Look for definitions related to random variables.
Question 2
Easy
If Cov(X,Y) = 0, what can we infer about the relationship between X and Y?
💡 Hint: Think about the implications of zero covariance.
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
True or False: Independence of random variables means they have covariance of zero.
- True
- False
💡 Hint: Remember the distinction between independence and correlation.
Question 2
What indicates that two variables are independent?
- Zero covariance
- Non-zero covariance
- Zero mutual information
- Same variance
💡 Hint: Link mutual information to independence.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Two random variables X and Y are defined with specific joint distributions. Calculate Cov(X,Y) and argue whether they might be independent.
💡 Hint: Use the definitions and calculate accordingly.
Question 2
Find a real-world scenario in communication systems where mutual information would be integral. Discuss its implications on the system design.
💡 Hint: Consider how signals and noise interactions might offer insights.
Challenge and get performance evaluation