Practice Worked Example (continuous Case) (15.6) - Marginal Distributions

Practice: Worked Example (Continuous Case)

Lesson 15.6Marginal Distributions

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6 sample questions

Question 1.
What does the joint pdf represent in probability theory?
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Think about how two random variables can interact.
Question 2.
What is the integral used for when finding marginal distributions?
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Recall the definition of marginalization.
3Question 3.
What does the marginal distribution of a variable express?
- The distribution of the entire population
- The distribution of a single variable
- ignoring others
- Only the joint probability
- The probability distribution over a range of data
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Think of how we analyze one aspect at a time.
4Question 4.
True or False: You can always reconstruct joint pdfs from marginal distributions if the variables are dependent.
- True
- False
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Consider the definition of dependency.
Question 5.
Consider the joint pdf f(x,y) = 4x^2y^2 for 0 < x < 1, 0 < y < 1. Derive both marginal distributions.
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Remember to integrate over the other variable to calculate each marginal.
Question 6.
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.
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Revisit the definition of independence and how it applies to our findings.

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