7.1.1 - Random Variables and Probability Distributions
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
What is a random variable?
💡 Hint: Think of it as a representation of outcomes in numbers.
Define a discrete random variable.
💡 Hint: Consider examples like dice rolls or number of students.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is the normalization condition for a PDF?
💡 Hint: Consider how probabilities relate to areas in geometry.
True or false: CDF can give the probability of a random variable being greater than a specific value.
💡 Hint: Think about what CDF shows and what it doesn't.
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
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!
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.