14.2 - Properties of Joint Distributions
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Practice Questions
Test your understanding with targeted questions
What does the term joint probability distribution refer to?
💡 Hint: Think about how we describe events happening at the same time.
True or False: In a joint distribution, probabilities can be negative.
💡 Hint: Consider the properties of probabilities.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the joint distribution of two random variables measure?
💡 Hint: Consider what 'joint' implies.
True or False: The total area under a joint PDF equals 1.
💡 Hint: Think about the properties of how probabilities are represented.
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Challenge Problems
Push your limits with advanced challenges
Consider three random variables: X, Y, and Z with a joint PMF defined at specific points. Demonstrate how to verify whether it's valid based on the non-negativity and normalization properties.
💡 Hint: It's about verifying all conditions are met.
A joint pdf is given as f(x,y) = Kxy for 0 < x < 1 and 0 < y < 1. Find the value of K for normalization.
💡 Hint: Use double integration for continuous variables!
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