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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the marginal pmf of X if the joint pmf p(x,y) = 0.2 for (x=0,y=1) and p(0,2) = 0.3?
💡 Hint: Remember to sum probabilities across possible values of Y.
Question 2
Easy
Define marginal distribution in your own words.
💡 Hint: Think about focusing on one variable only.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the formula for the marginal pmf of X?
- p(x) = ∑ p(x,y)
- p(x) = ∫ p(x,y) dy
- p(x) = p(x,y) - p(y)
💡 Hint: Focus on how we isolate one variable.
Question 2
True or False: Marginal distributions can always be used to reconstruct the joint distribution.
- True
- False
💡 Hint: Consider if independence is necessary for reconstruction.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Consider the joint pmf for two discrete random variables: p(0,0)=0.3, p(0,1)=0.1, p(1,0)=0.4, and p(1,1)=0.2. Calculate the marginal distribution for both variables.
💡 Hint: Sum probabilities for each variable correctly.
Question 2
If the two variables X and Y are independent, deduce the relationship of their joint pmf to their marginal pmfs mathematically.
💡 Hint: Reflect on definitions of independence.
Challenge and get performance evaluation