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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the definition of independence in random variables?
💡 Hint: Think about the relationship between probabilities.
Question 2
Easy
Give an example of independent random variables in real life.
💡 Hint: Consider scenarios where one event does not influence the other.
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
If P(X=x, Y=y) = P(X=x) * P(Y=y), what can we say about X and Y?
- They are dependent
- They are independent
- Not enough information
💡 Hint: Consider the implications of the joint probability.
Question 2
True or False: Independence of random variables means that their expected values can be treated independently.
- True
- False
💡 Hint: Think about how expected values are combined for independent variables.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Consider two continuous random variables X and Y with joint PDF f(x, y) = e^(-x) * e^(-y). Verify if they are independent.
💡 Hint: Look closely how you can factor the joint PDF.
Question 2
In a certain communication system, noise variables N1 and N2 are modeled as independent. If both have a mean of 0 and variance of 1, what can be said about their influence on the total noise N = N1 + N2?
💡 Hint: Remember the properties of independent random variables.
Challenge and get performance evaluation