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CDF: F<sub>X</sub>(x) = <math>1-e^{-\lambda*x}</math> | CDF: F<sub>X</sub>(x) = <math>1-e^{-\lambda*x}</math> | ||
| + | |||
| + | |||
| + | PDF Properties | ||
| + | * <math> f_X(x)\geq 0 </math> for all x | ||
| + | * <math> \int\limits_{-\infty}^{\infty}f_X(x)dx = 1</math> | ||
| + | * If <math> \delta </math> is very small, then | ||
| + | <math> P([x,x+\delta]) \approx f_X(x)\cdot\delta</math> | ||
| + | * For any subset B of the real line, | ||
| + | <math> P(X\in B) = \int\limits_Bf_X(x)dx </math> | ||
Revision as of 07:27, 20 October 2008
Cumulative Density Function (CDF)
- FX(x) = P(X <= x) = integral(-inf to inf) fX(y) dy
- 1 - FX(x) = P(X > x)
Exponential RV
PDF: fX(x) = $ \lambda*e^{-\lambda*x} $, x >= 0 ; fX(x) = 0 , else
CDF: FX(x) = $ 1-e^{-\lambda*x} $
PDF Properties
- $ f_X(x)\geq 0 $ for all x
- $ \int\limits_{-\infty}^{\infty}f_X(x)dx = 1 $
- If $ \delta $ is very small, then
$ P([x,x+\delta]) \approx f_X(x)\cdot\delta $
- For any subset B of the real line,
$ P(X\in B) = \int\limits_Bf_X(x)dx $
