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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What does PDF stand for?
💡 Hint: Recall the acronym we discussed.
Question 2
Easy
What property ensures the area under a PDF equals one?
💡 Hint: Think about the key requirements 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 property must a PDF satisfy?
- It can be negative
- The total area under the curve is 0
- The total area under the curve is 1
💡 Hint: Consider what makes a valid probability distribution.
Question 2
Is the mean of a random variable always zero?
- True
- False
💡 Hint: Think about different types of distributions.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a continuous random variable with PDF f(x) = 12x(1-x) for 0 ≤ x ≤ 1, find the probability that X falls between 0.25 and 0.75.
💡 Hint: Refer to integration techniques for polynomials.
Question 2
Calculate the expected value (mean) of X when its PDF is given as f(x) = 6x(1-x) for 0 ≤ x ≤ 1.
💡 Hint: Distributing and integrating will be key here.
Challenge and get performance evaluation