Practice Solved Examples (13.1.7) - Probability Density Function (pdf)

Practice: Solved Examples

Lesson 13.1.7Probability Density Function (pdf)

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6 sample questions

Question 1.
What is a Probability Density Function?
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Think about how probabilities are represented for continuous variables.
Question 2.
In a uniform distribution, is the probability of every outcome the same?
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Consider how a flat curve looks on a graph!
3Question 3.
What does a Probability Density Function represent?
- Probabilities at discrete points
- Probabilities over intervals
- Only the mean value
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Think about how continuous distributions work!
4Question 4.
True or False: The total area under a PDF equals 1.
- True
- False
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Consider the normalization property of PDFs.
Question 5.
Given a PDF f(x) = 3x^2 for 0 ≤ x ≤ 1, calculate E[X] and P(X < 0.5).
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Use the integration formula carefully for both calculations.
Question 6.
A random variable X follows a triangular distribution with PDF f(x) = 2x for 0 ≤ x ≤ 1. Find the probability P(0.3 ≤ X ≤ 0.7) and the expected value E[X].
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Set your integration limits appropriately based on the PDF.

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