Practice Properties (7.2.3.1) - Probability Distribution Function (PDF)

Practice: Properties

Lesson 7.2.3.1Probability Distribution Function (PDF)

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9 questions

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6 sample questions

Question 1.
What does the non-negativity property of a PDF state?
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Think about what probabilities can be.
Question 2.
Write the formula that expresses normalization for a PDF.
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Consider the area under the PDF curve.
3Question 3.
What does the non-negativity property of a PDF imply?
- Probabilities can be negative
- Probabilities must be zero or greater
- Probabilities sum to one
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Reflect on the fundamental nature of probabilities.
4Question 4.
True or False: The integral of a PDF over its entire range must equal one.
- True
- False
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Consider what it means for a total probability.
Question 5.
Given a PDF defined as $f(x) = 3(1-x)^2$ for 0 ≤ x ≤ 1, determine whether it is a valid PDF and calculate its mean.
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First, ensure the PDF meets the properties.
Question 6.
If the variance of a random variable is known to be 4 and the mean is 5, what can you infer about the dispersion of data points?
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Consider how variance represents spread from the mean.

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