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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a PDF?
💡 Hint: Think of how probabilities are represented for continuous outcomes.
Question 2
Easy
Is the probability of a continuous variable taking a specific value greater than zero?
💡 Hint: Consider how probabilities are defined for intervals.
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 is a Probability Density Function?
- A function for discrete outcomes
- A function for continuous outcomes
- Neither of the above
💡 Hint: Remember the definitions of different types of functions.
Question 2
True or False: The probability of a continuous random variable taking a specific value is greater than zero.
- True
- False
💡 Hint: Review how probabilities are defined.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a PDF f(x) = 3x² for 0 ≤ x ≤ 1, verify that it is a valid PDF and find E[X].
💡 Hint: Use integration techniques to confirm area and moments.
Question 2
If the variance is given by Var(X) = ∫ (x - E[X])² * f(x) dx, compute the Variance for f(x) = 1/5 for 0 ≤ x ≤ 5.
💡 Hint: Remember to use integration for both components of variance calculation.
Challenge and get performance evaluation