13.1 - Probability Density Function (PDF)
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Practice Questions
Test your understanding with targeted questions
What is a PDF?
💡 Hint: Think of how probabilities are represented for continuous outcomes.
Is the probability of a continuous variable taking a specific value greater than zero?
💡 Hint: Consider how probabilities are defined for intervals.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is a Probability Density Function?
💡 Hint: Remember the definitions of different types of functions.
True or False: The probability of a continuous random variable taking a specific value is greater than zero.
💡 Hint: Review how probabilities are defined.
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
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.
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