13.1.2 - What is a Probability Density Function (PDF)?
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Practice Questions
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Define what a PDF is in your own words.
💡 Hint: Think about how we visualize probabilities over intervals.
What is the total probability in any PDF?
💡 Hint: Recall the property of normalization.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does a PDF describe?
💡 Hint: Think about the characteristics of continuous versus discrete.
The total area under the PDF curve for a continuous random variable is equal to:
💡 Hint: Remember the normalization property.
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Challenge Problems
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Suppose a PDF is defined as f(x) = 3x^2 for 0 ≤ x ≤ 1. Calculate the probability that X falls between 0.2 and 0.5.
💡 Hint: Remember to set up the integral properly and evaluate it.
Given a normal distribution with mean 10 and variance 4, calculate the probability that a random variable X is less than 12.
💡 Hint: Transform the problem to fit the standard normal distribution format.
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