What does it mean to normalise a frequency distribution to obtain a Probability Density Function (PDF)?
Understand the Problem
The question asks about the meaning of normalizing a frequency distribution to obtain a Probability Density Function (PDF). It presents four options, and we need to identify the correct one.
Answer
It means scaling frequencies so the total area under the density curve equals 1, creating a valid probability distribution.
Normalizing a frequency distribution to obtain a Probability Density Function (PDF) involves scaling the frequencies so that the total area under the resulting density curve equals 1. This ensures the PDF represents a valid probability distribution.
Answer for screen readers
Normalizing a frequency distribution to obtain a Probability Density Function (PDF) involves scaling the frequencies so that the total area under the resulting density curve equals 1. This ensures the PDF represents a valid probability distribution.
More Information
A PDF is always non-negative, and the integral of the PDF over all possible values must equal 1.
Tips
A common mistake is to confuse the PDF with the actual probability. The PDF value at a point is a density, not a probability. The probability is found by integrating the PDF over an interval.
Sources
- Probability Density Function(PDF): Definition, Formula, Example - geeksforgeeks.org
- Probability density function - Wikipedia - en.wikipedia.org
- [PDF] Chapter 2. Random Variables and Probability Distributions - utkstair.org
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