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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the definition of independent random variables?
💡 Hint: Think about the relationship between their outcomes.
Question 2
Easy
Give an example of two independent continuous random variables.
💡 Hint: Consider measurements that do not interfere with each 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
Two random variables X and Y are independent if:
- f(X,Y) = f(X) + f(Y)
- f(X,Y) = f(X) * f(Y)
- f(X,Y) = f(X) - f(Y)
💡 Hint: Remember the formula for independence.
Question 2
If f(X,Y) is not equal to f(X) * f(Y), then X and Y are:
- True
- False
💡 Hint: Think about the condition for independence.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Suppose X and Y have joint PDF given as f(X,Y) = 1/(2πσ^2)e^(-((X-μ_x)^2+(Y-μ_y)^2)/(2σ^2)) for X,Y in ℝ. Prove if X and Y are independent.
💡 Hint: Focus on calculating the marginals carefully.
Question 2
In a study, varX and varY are found to be independent with PDFs being non-overlapping across all domains. Discuss the implications on their expected values.
💡 Hint: Reflect on how independence affects the products of expectations.
Challenge and get performance evaluation