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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a discrete random variable with an example.
💡 Hint: Think of something that can be counted.
Question 2
Easy
What is a joint probability distribution?
💡 Hint: Consider how two dice rolls might relate.
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 a random variable?
💡 Hint: Remember the connection to probability outcomes.
Question 2
For discrete random variables, what must the joint pmf always satisfy?
- Must be negative
- Must equal to 2
- Must sum up to 1
💡 Hint: Think about the total probability.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a joint pmf for two discrete random variables X and Y, calculate the marginal pmfs and check independence from the provided joint distribution.
💡 Hint: Look for the sums to equal 1 and the independence equalities.
Question 2
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.
💡 Hint: Remember the special properties of the normal distribution.
Challenge and get performance evaluation