15 - Partial Differential Equations
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Practice Questions
Test your understanding with targeted questions
What is the joint probability density function (pdf)?
💡 Hint: Think about how two random events relate.
Define marginal distribution.
💡 Hint: What do we focus on when we 'marginalize'?
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a marginal distribution?
💡 Hint: Think about the process of simplifying.
True or False: Marginal distributions can reconstruct joint distributions.
💡 Hint: Consider independence in your reasoning.
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Challenge Problems
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Given the joint pdf 𝑓(𝑥,𝑦) = 12𝑥𝑦 for 0 < 𝑥 < 1 and 0 < 𝑦 < 1, calculate the marginal distributions of 𝑋 and 𝑌.
💡 Hint: Focus on integrating each variable's contribution.
Discuss the independence condition for two random variables and provide an example illustrating this with marginal pdfs.
💡 Hint: Consider if separating their probabilities affects their joint behavior.
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