17.7 - Tests and Theorems Related to Independence
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Practice Questions
Test your understanding with targeted questions
What does it mean for two random variables to be independent?
💡 Hint: Look for definitions related to random variables.
If Cov(X,Y) = 0, what can we infer about the relationship between X and Y?
💡 Hint: Think about the implications of zero covariance.
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Interactive Quizzes
Quick quizzes to reinforce your learning
True or False: Independence of random variables means they have covariance of zero.
💡 Hint: Remember the distinction between independence and correlation.
What indicates that two variables are independent?
💡 Hint: Link mutual information to independence.
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Challenge Problems
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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.
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.
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