7.2.3.1 - Properties
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 does the non-negativity property of a PDF state?
💡 Hint: Think about what probabilities can be.
Write the formula that expresses normalization for a PDF.
💡 Hint: Consider the area under the PDF curve.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What does the non-negativity property of a PDF imply?
💡 Hint: Reflect on the fundamental nature of probabilities.
True or False: The integral of a PDF over its entire range must equal one.
💡 Hint: Consider what it means for a total probability.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Given a PDF defined as $$f(x) = 3(1-x)^2$$ for 0 ≤ x ≤ 1, determine whether it is a valid PDF and calculate its mean.
💡 Hint: First, ensure the PDF meets the properties.
If the variance of a random variable is known to be 4 and the mean is 5, what can you infer about the dispersion of data points?
💡 Hint: Consider how variance represents spread from the mean.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.