1.7 CDF (Cumulative Distribution Function) and PDF (Probability Density Function)
From the ECE600 Pre-requisites notes of Sangchun Han, ECE PhD student.
$ F_{\mathbf{X}}\left(x\right)=P\left(\left\{ \mathbf{X}\leq x\right\} \right) $
$ f_{\mathbf{X}}\left(x\right)=\frac{d}{dx}F_{\mathbf{X}}\left(x\right) $
Valid PDF
1. $ f_{\mathbf{X}}\left(x\right)\geq0,\;\forall x\in\mathbf{R} $
2. $ \int_{-\infty}^{\infty}f_{\mathbf{X}}\left(x\right)dx=1 $
