13.1.6 - Mean and Variance using PDF
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 the expected value of a continuous random variable with PDF f(x) = 3x² for x from 0 to 1?
💡 Hint: Use the integral definition of expected value.
Define variance.
💡 Hint: Think about variability in data.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is the formula for calculating the mean of a continuous random variable?
💡 Hint: Focus on what you integrate.
True or False: Variance can be zero for a random variable.
💡 Hint: Consider what variance measures.
1 more question available
Challenge Problems
Push your limits with advanced challenges
A continuous random variable's PDF is given by f(x) = 12x(1-x) for 0 ≤ x ≤ 1. Calculate the mean and variance.
💡 Hint: Calculate the mean first and then use it to find the variance.
For a normal distribution with mean 5 and standard deviation 2, determine E[X²] and its relationship to the variance.
💡 Hint: Recall the formulas relating mean and variance.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.