14.3.2 - Marginal PDF (Continuous)
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Practice Questions
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What is the marginal PDF of X if the joint PDF is f(x,y) = 6xy for 0 ≤ x, y ≤ 1?
💡 Hint: Integrate 6xy with respect to y from 0 to 1.
State the condition for marginal PDFs in relation to joint PDFs.
💡 Hint: Consider the definition of probability density functions.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the marginal PDF represent?
💡 Hint: Think about the term 'marginal' and its meaning in statistics.
Integration is used to find marginal PDFs because it allows for:
💡 Hint: Recall the purpose of integration in mathematics.
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Challenge Problems
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Given the joint probability density function f(x,y) = 3x^2y for 0
💡 Hint: Check your limits and ensure proper integration across defined boundaries.
A researcher calculates the marginal PDF of X as f_X(x)=x^2 for x≥0. If the joint PDF integrates to 1, what does it indicate about Y?
💡 Hint: Remember that joint distributions always require summation to 1 across all dimensions.
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