(New page: ='''1.7 CDF (Cumulative Distribution Function) and PDF (Probability Density Function)'''= <math>F_{\mathbf{X}}\left(x\right)=P\left(\left\{ \mathbf{X}\leq x\right\} \right)</math> <math...) |
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='''1.7 CDF (Cumulative Distribution Function) and PDF (Probability Density Function)'''= | ='''1.7 CDF (Cumulative Distribution Function) and PDF (Probability Density Function)'''= | ||
| − | + | From the [[ECE_600_Prerequisites|ECE600 Pre-requisites notes]] of [[user:han84|Sangchun Han]], [[ECE]] PhD student. | |
| + | ---- | ||
<math>F_{\mathbf{X}}\left(x\right)=P\left(\left\{ \mathbf{X}\leq x\right\} \right)</math> | <math>F_{\mathbf{X}}\left(x\right)=P\left(\left\{ \mathbf{X}\leq x\right\} \right)</math> | ||
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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 class="inline">\int_{-\infty}^{\infty}f_{\mathbf{X}}\left(x\right)dx=1</math> | ||
| + | ---- | ||
| + | [[ECE600|Back to ECE600]] | ||
| − | + | [[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 $
