17.2.1 - Joint Probability Mass Function (PMF)
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Practice Questions
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Define a Joint Probability Mass Function.
💡 Hint: Think of it as a function relating two outcomes.
Give an example of a discrete random variable.
💡 Hint: Focus on countable outcomes.
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Interactive Quizzes
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What does Joint PMF indicate?
💡 Hint: Think about the combined outcomes.
True or False: If two random variables are independent, their joint PMF can be expressed as the product of their individual PMFs.
💡 Hint: Recall the independence formula we discussed.
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Challenge Problems
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You are given a joint PMF where P(X=1, Y=1)=0.5, P(X=1, Y=2)=0.3, and P(X=2, Y=2)=0.2. Check if X and Y are independent.
💡 Hint: Sum the probabilities to find marginal values first.
You have P(X=1, Y=1)=0.25, P(X=1, Y=2)=0.25, P(X=2, Y=1)=0.25, P(X=2, Y=2)=0.25. Are X and Y independent?
💡 Hint: This illustrates proper checking for equality in independence.
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