Practice Examples - 17.5 | 17. Independence of Random Variables | Mathematics - iii (Differential Calculus) - Vol 3
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17.5 - Examples

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What does it mean for random variables to be independent?

💡 Hint: Think of the dice examples we discussed.

Question 2 Easy

How is the joint PMF represented for discrete random variables?

💡 Hint: Refer to the table format presented in our example.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What indicates that two random variables are independent?

P(X,Y) = P(X) * P(Y)
P(X,Y) < P(X) * P(Y)
P(X,Y) > P(X) * P(Y)

💡 Hint: Anchor this to the conditional probabilities we discussed.

Question 2

In discrete random variables, which function describes the joint probabilities?

Marginal Probability Function
Joint Probability Mass Function
Mutual Information

💡 Hint: Check the terminology we used before.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given X and Y with the joint PDF f(x,y) = e^(-x) * e^(-y), derive whether X and Y are independent.

💡 Hint: Calculate the marginal PDFs first.

Challenge 2 Hard

Create a joint PMF for X and Y that showcases independence and calculate all relevant probabilities.

💡 Hint: Make sure distributions sum to 1 and check independence condition afterward.

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