15.6 - Worked Example (Continuous Case)
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Practice Questions
Test your understanding with targeted questions
What does the joint pdf represent in probability theory?
💡 Hint: Think about how two random variables can interact.
What is the integral used for when finding marginal distributions?
💡 Hint: Recall the definition of marginalization.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the marginal distribution of a variable express?
💡 Hint: Think of how we analyze one aspect at a time.
True or False: You can always reconstruct joint pdfs from marginal distributions if the variables are dependent.
💡 Hint: Consider the definition of dependency.
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Challenge Problems
Push your limits with advanced challenges
Consider the joint pdf f(x,y) = 4x^2y^2 for 0 < x < 1, 0 < y < 1. Derive both marginal distributions.
💡 Hint: Remember to integrate over the other variable to calculate each marginal.
Given a joint pdf f(x,y) = xy for 0 < x < 2 and 0 < y < 2, analyze its marginal distributions and check if the variables are independent.
💡 Hint: Revisit the definition of independence and how it applies to our findings.
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