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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 it as a representation of outcomes in numbers.
Question 2
Easy
Define a discrete random variable.
💡 Hint: Consider examples like dice rolls or number of students.
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 normalization condition for a PDF?
💡 Hint: Consider how probabilities relate to areas in geometry.
Question 2
True or false: CDF can give the probability of a random variable being greater than a specific value.
- True
- False
💡 Hint: Think about what CDF shows and what it doesn't.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A continuous random variable has a PDF defined as f(x) = kx for 0 ≤ x ≤ 2. Find the value of k and then the probability that X < 1.
💡 Hint: Remember to normalize the PDF first, then use integration.
Question 2
The mean of a random variable X is defined by the integral μ = ∫ x f(x) dx. For the PDF f(x) = 2x (0 ≤ x ≤ 1), calculate the mean.
💡 Hint: The integration step is crucial for finding the expected value!
Challenge and get performance evaluation