17.5 - Examples
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Practice Questions
Test your understanding with targeted questions
What does it mean for random variables to be independent?
💡 Hint: Think of the dice examples we discussed.
How is the joint PMF represented for discrete random variables?
💡 Hint: Refer to the table format presented in our example.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What indicates that two random variables are independent?
💡 Hint: Anchor this to the conditional probabilities we discussed.
In discrete random variables, which function describes the joint probabilities?
💡 Hint: Check the terminology we used before.
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Challenge Problems
Push your limits with advanced challenges
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.
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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Reference links
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