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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a Probability Density Function (PDF).
💡 Hint: Think about how we express probabilities for continuous variables.
Question 2
Easy
What is the definition of non-negativity in the context of PDFs?
💡 Hint: Consider the graphical representation of a PDF.
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 describes the likelihood of a continuous random variable taking on a particular value?
- Probability Mass Function
- Probability Density Function
- Cumulative Distribution Function
💡 Hint: Think about continuous random variables.
Question 2
The total area under a PDF curve equals what?
- True
- False
💡 Hint: Consider how probabilities relate to areas.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A continuous random variable X follows a PDF given by f(x) = 2x for 0 ≤ x ≤ 1. Calculate the expected value E[X] and the variance Var(X).
💡 Hint: Set up your integrals carefully and simplify appropriately.
Question 2
Given a normal distribution with mean μ = 0 and variance σ² = 1, compute the probability that a value lies between -1 and 1 using the standard normal table.
💡 Hint: Consider how the area under the curve represents probabilities.
Challenge and get performance evaluation