Probability Density Function

Probability density functions are used to define the distributions of continuous random variables $X:\Omega \to \mathbb{R}$. We use the following definitions.

Statements

Definition. The probability density function (PDF) of a continuous Random Variable is defined as a function $p_X:\mathbb{R}\to\mathbb{R}_{\geq0}$$ with the properties

1. ${\int }_{\mathbb{R}}{p}_X(x)dx=1$
2. $p_X(x_1\le x\le x_2)={\int }_{x_1}^{x_2}{p}_X(x)dx,\forall x_1,x_2\in \mathbb{R}$ with $x_1\le x_2$.

References

D. Ostwald - The general linear model 20_21

Probability density function - Wikipedia