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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Explain what non-negativity means in the context of PDFs.
💡 Hint: Think about the concept of probability.
Question 2
Easy
What is normalization of a PDF?
💡 Hint: Consider how probabilities should sum up.
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 normalization ensure for a PDF?
- Total probability equals zero
- Total probability equals one
- PDF values can be negative
💡 Hint: Remember that probabilities must always have a sum.
Question 2
True or False: The mean of a random variable gives us its most common value.
- True
- False
💡 Hint: Consider what average means versus frequency.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
If a PDF is given as f(x) = 1/2 for 0 ≤ x ≤ 2, calculate the mean and variance.
💡 Hint: You may use integration techniques.
Question 2
Find the probability that a random variable X, described by the PDF f(x) = 3x² for 0 ≤ x ≤ 1, lies between 0.5 and 1.
💡 Hint: Remember to set up your integral limits correctly.
Challenge and get performance evaluation