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='''Valid PDF'''= | ='''Valid PDF'''= | ||
| − | 1. <math>f_{\mathbf{X}}\left(x\right)\geq0,\;\forall x\in\mathbf{R}</math> | + | 1. <math class="inline">f_{\mathbf{X}}\left(x\right)\geq0,\;\forall x\in\mathbf{R}</math> |
| − | 2. <math>\int_{-\infty}^{\infty}f_{\mathbf{X}}\left(x\right)dx=1</math> | + | 2. <math class="inline">\int_{-\infty}^{\infty}f_{\mathbf{X}}\left(x\right)dx=1</math> |
---- | ---- | ||
[[ECE600|Back to ECE600]] | [[ECE600|Back to ECE600]] | ||
[[ECE 600 Prerequisites|Back to ECE 600 Prerequisites]] | [[ECE 600 Prerequisites|Back to ECE 600 Prerequisites]] | ||
Latest revision as of 11:29, 30 November 2010
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 $
