PDF

159. PDF

159.1. PDF (Probability Density Function)

Function that describes the likelihood of a continuous random variable taking on a particular value

Properties:

The area under the curve of a PDF over the entire range of possible values equals 1
The PDF itself is non-negative everywhere
The probability that the variable falls within a certain range is given by the integral of the PDF over that range

159.1.1. Relationship to the CDF

The PDF is the derivative of the CDF; integrating the PDF back recovers the CDF:

𝑓 (𝑥) = \frac{d}{d 𝑥} 𝐹 (𝑥) ⟺ 𝐹 (𝑥) = \int_{- \infty}^{𝑥} 𝑓 (𝑡) d 𝑡