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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a Probability Density Function?
💡 Hint: Think about how probabilities are represented for continuous variables.
Question 2
Easy
In a uniform distribution, is the probability of every outcome the same?
💡 Hint: Consider how a flat curve looks on a graph!
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 does a Probability Density Function represent?
- Probabilities at discrete points
- Probabilities over intervals
- Only the mean value
💡 Hint: Think about how continuous distributions work!
Question 2
True or False: The total area under a PDF equals 1.
- True
- False
💡 Hint: Consider the normalization property of PDFs.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation