Practice Definitions And Basics (14.1) - Joint Probability Distributions

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6 sample questions

Question 1.
Define a discrete random variable with an example.
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Think of something that can be counted.
Question 2.
What is a joint probability distribution?
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Consider how two dice rolls might relate.
3Question 3.
What is a random variable?
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Remember the connection to probability outcomes.
4Question 4.
For discrete random variables, what must the joint pmf always satisfy?
- Must be negative
- Must equal to 2
- Must sum up to 1
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Think about the total probability.
Question 5.
Given a joint pmf for two discrete random variables X and Y, calculate the marginal pmfs and check independence from the provided joint distribution.
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Look for the sums to equal 1 and the independence equalities.
Question 6.
We have X ~ N(0, σ²) and Y ~ N(0, σ²) as jointly normal random variables. Show that X and Y being uncorrelated implies independence.
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Remember the special properties of the normal distribution.

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