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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define independence of random variables.
💡 Hint: Think about how one variable's outcome impacts another.
Question 2
Easy
Given P(X=2) = 0.3, P(Y=3) = 0.5, calculate P(X=2, Y=3) if X and Y are independent.
💡 Hint: Use the formula for the joint probability of independent events.
Practice 1 more question 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 definition of independence in probability?
💡 Hint: Consider the influence one variable has over another.
Question 2
If P(X=1) = 0.4 and P(Y=2) = 0.6, what is P(X=1, Y=2) if X and Y are independent?
- 0.24
- 0.10
- 0.20
💡 Hint: Multiply the individual probabilities of X and Y.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A fair die is rolled twice. What is the probability of rolling a two on the first roll and a three on the second? Are these events independent?
💡 Hint: Use the independence formula for joint probabilities.
Question 2
If X and Y are independent random variables with P(X=1) = 0.2 and P(Y=1) = 0.5, what is P(X=1, Y=1)? Are they independent?
💡 Hint: Apply the independence condition to find joint probabilities.
Challenge and get performance evaluation