Practice Discrete Case (15.3) - Marginal Distributions - Mathematics - iii (Differential Calculus) - Vol 3

Practice: Discrete Case

Lesson 15.3Marginal Distributions

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9 questions

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6 sample questions

Question 1.
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?
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Remember to sum probabilities across possible values of Y.
Question 2.
Define marginal distribution in your own words.
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Think about focusing on one variable only.
3Question 3.
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)
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Focus on how we isolate one variable.
4Question 4.
True or False: Marginal distributions can always be used to reconstruct the joint distribution.
- True
- False
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Consider if independence is necessary for reconstruction.
Question 5.
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.
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Sum probabilities for each variable correctly.
Question 6.
If the two variables X and Y are independent, deduce the relationship of their joint pmf to their marginal pmfs mathematically.
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Reflect on definitions of independence.

5 more questions in this section. Enroll free to practise them all.