Practice Marginal Distributions (14.3) - Joint Probability Distributions

Practice: Marginal Distributions

Lesson 14.3Joint Probability Distributions

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9 questions

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6 sample questions

Question 1.
What is the formula for the marginal PMF of X in a discrete joint distribution?
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Think of summing over the probabilities in the joint PMF.
Question 2.
In continuous distributions, what do we do to find the marginal PDF of X?
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Integration will help you collapse the other variable.
3Question 3.
What does a marginal distribution refer to in probability theory?
- The overall distribution of multiple variables
- The distribution of a single variable
- The joint distribution of two variables
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Focus on the term 'marginal' which indicates focusing on one aspect.
4Question 4.
True or False: Marginal distributions can only be derived from discrete random variables.
- True
- False
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Consider the definitions of marginals for different types of random variables.
Question 5.
In a joint distribution of two dice rolls, what is the marginal distribution of one die? Provide a detailed explanation of your process.
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Start with a joint probability table, then aggregate relevant entries.
Question 6.
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.
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Evaluate the integrals correctly and then set up their products.

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