Practice Independence and Marginals - 15.8 | 15. Marginal Distributions | Mathematics - iii (Differential Calculus) - Vol 3
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Independence and Marginals

15.8 - Independence and Marginals

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define independence between two random variables.

💡 Hint: Think of how one variable's value affects another.

Question 2 Easy

What is a marginal distribution?

💡 Hint: Consider how to isolate one variable from a joint distribution.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does it mean for two variables to be independent?

They are always the same
Knowing one gives no information about the other
They depend on each other

💡 Hint: Recall the definition of independence.

Question 2

If f(x, y) = f(x) * f(y), what does that indicate?

True
False

💡 Hint: Look at the properties of joint distributions.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

You have two random variables: X, representing the time taken to finish a project, and Y, representing the number of meetings held. If their joint pdf is given, explain how you would prove or disprove their independence.

💡 Hint: Focus on how the integration works.

Challenge 2 Hard

A communication engineer observes that signal strength and background noise behave independently based on their joint distribution. Describe the analysis process using independence.

💡 Hint: What do you compare to check independence?

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