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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a random variable.
💡 Hint: Think about the outcomes of a certain experiment.
Question 2
Easy
What does a Probability Mass Function (PMF) describe?
💡 Hint: What type of variable is countable?
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 the definition of independent random variables?
- They influence each other's distribution
- They do not affect each other's probabilities
- They must have the same mean
💡 Hint: Think about how one event might not influence another.
Question 2
For discrete variables, P(X=x, Y=y) = P(X=x) * P(Y=y) holds true if they are independent. True or False?
- True
- False
💡 Hint: Recall the definition you studied.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a joint distribution P(X,Y) = P(X)P(Y) where P(X=1) = 0.5, P(Y=1)=0.4, find P(X=1, Y=1).
💡 Hint: Think about using the independence condition.
Question 2
Prove that two random variables are dependent if P(X=x,Y=y) does not equal P(X=x)P(Y=y).
💡 Hint: Consider cases where the multiplication law fails.
Challenge and get performance evaluation