14.8 - Example Problems
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Practice Questions
Test your understanding with targeted questions
What is the marginal PMF of X for the discrete distribution given?
💡 Hint: Sum the probabilities where X equals 0.
How can you check if two random variables X and Y are independent?
💡 Hint: Use the joint PMF for verification.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the joint probability mass function define?
💡 Hint: Think about how they relate to each other.
True or False: Marginal distributions can always be derived from joint distributions.
💡 Hint: Recall the method of finding marginals.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Consider a random variable Z defined with a joint PMF across three dimensions. Determine the marginal PMF for Z and check if it influences the independence of the two other dimensions.
💡 Hint: Break the problem down dimension by dimension!
Given a continuous distribution defined in a non-standard region, derive its joint PDF and confirm its validity before calculating marginal PDFs.
💡 Hint: Focus on region boundaries for proper limits!
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