14.1.2 - Joint Probability Distribution
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Practice Questions
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Define Joint PMF.
💡 Hint: Think of it as the probability table for two variables.
What do we call the probability of one variable independent of another?
💡 Hint: Remember, it's about the influence of one on another.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the joint PMF represent?
💡 Hint: Focus on the word 'joint'.
True or False: If two random variables are independent, P(X, Y) = P(X) * P(Y).
💡 Hint: Think about their interaction.
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Challenge Problems
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Given a joint PMF where P(X=1, Y=0) = 0.2, P(X=1, Y=1) = 0.3, and all others are 0, compute marginal PMFs for X and Y.
💡 Hint: Look carefully at how you sum probabilities.
Consider a joint PDF f(x,y) = 2xy for 0 <= x <= 1 and 0 <= y <= 1. Confirm it is a valid PDF and find marginal PDFs for each variable.
💡 Hint: Check for area under the curve.
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