13.1.7 - Solved Examples
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 Probability Density Function?
💡 Hint: Think about how probabilities are represented for continuous variables.
In a uniform distribution, is the probability of every outcome the same?
💡 Hint: Consider how a flat curve looks on a graph!
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What does a Probability Density Function represent?
💡 Hint: Think about how continuous distributions work!
True or False: The total area under a PDF equals 1.
💡 Hint: Consider the normalization property of PDFs.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
Given a PDF f(x) = 3x^2 for 0 ≤ x ≤ 1, calculate E[X] and P(X < 0.5).
💡 Hint: Use the integration formula carefully for both calculations.
A random variable X follows a triangular distribution with PDF f(x) = 2x for 0 ≤ x ≤ 1. Find the probability P(0.3 ≤ X ≤ 0.7) and the expected value E[X].
💡 Hint: Set your integration limits appropriately based on the PDF.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.