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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a random variable?
💡 Hint: Think of what you measure in experiments.
Question 2
Easy
Can independent random variables affect each other's outcomes?
💡 Hint: Reflect on the concept of independence.
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
Two random variables are independent if:
- A) They have the same marginal distribution
- B) P(X = x
- Y = y) = P(X = x)P(Y = y)
- C) Cov(X
- Y) = 0
💡 Hint: Recall the definition of independence.
Question 2
If Cov(X, Y) = 0, then X and Y are definitely independent.
💡 Hint: Consider examples of uncorrelated but dependent variables.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Two people flip a coin simultaneously. Let A be the event of 'Person 1 gets heads' and B be 'Person 2 gets heads'. Are the events A and B independent? Justify your answer with probabilities.
💡 Hint: Consider the outcomes of independent events.
Question 2
Given two dice rolls defined as random variables X and Y, show whether they are independent if the results are analyzed via conditional probabilities.
💡 Hint: Think about how the outcome of each die is calculated.
Challenge and get performance evaluation