14.3 - Marginal Distributions
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Practice Questions
Test your understanding with targeted questions
What is the formula for the marginal PMF of X in a discrete joint distribution?
💡 Hint: Think of summing over the probabilities in the joint PMF.
In continuous distributions, what do we do to find the marginal PDF of X?
💡 Hint: Integration will help you collapse the other variable.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does a marginal distribution refer to in probability theory?
💡 Hint: Focus on the term 'marginal' which indicates focusing on one aspect.
True or False: Marginal distributions can only be derived from discrete random variables.
💡 Hint: Consider the definitions of marginals for different types of random variables.
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Challenge Problems
Push your limits with advanced challenges
In a joint distribution of two dice rolls, what is the marginal distribution of one die? Provide a detailed explanation of your process.
💡 Hint: Start with a joint probability table, then aggregate relevant entries.
Given a joint PDF of f(x,y) = 2x + 3y for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1, derive the marginal PDFs and verify if they support independence.
💡 Hint: Evaluate the integrals correctly and then set up their products.
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