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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What does the non-negativity property of a PDF state?
💡 Hint: Think about what probabilities can be.
Question 2
Easy
Write the formula that expresses normalization for a PDF.
💡 Hint: Consider the area under the PDF curve.
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 the non-negativity property of a PDF imply?
- Probabilities can be negative
- Probabilities must be zero or greater
- Probabilities sum to one
💡 Hint: Reflect on the fundamental nature of probabilities.
Question 2
True or False: The integral of a PDF over its entire range must equal one.
- True
- False
💡 Hint: Consider what it means for a total probability.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation