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! style="background: rgb(238, 238, 238) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;" colspan="2" | Cauchy-schwarz Inequality | ! style="background: rgb(238, 238, 238) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;" colspan="2" | Cauchy-schwarz Inequality | ||
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| align="right" style="padding-right: 1em;" | Uniform random variable over (a,b) | | align="right" style="padding-right: 1em;" | Uniform random variable over (a,b) | ||
| <math>\,E[X] = \frac{a+b}{2},\ \ Var(X) = \frac{(b-a)^2}{12}\,</math> | | <math>\,E[X] = \frac{a+b}{2},\ \ Var(X) = \frac{(b-a)^2}{12}\,</math> | ||
Revision as of 11:38, 22 November 2010
| Inequalities | |
|---|---|
| Triangulare Inequalities | |
| The complement of an event A (i.e. the event A not occurring) | $ \,P(A^c) = 1 - P(A)\, $ |
| Cauchy-schwarz Inequality | |
| Uniform random variable over (a,b) | $ \,E[X] = \frac{a+b}{2},\ \ Var(X) = \frac{(b-a)^2}{12}\, $ |
| Gaussian random variable with parameter $ \mu \mbox{ and } \sigma^2 $ | $ \,E[X] = \mu,\ \ Var(X) = \sigma^2\, $ |
| Exponential random variable with parameter $ \lambda $ | $ \,E[X] = \frac{1}{\lambda},\ \ Var(X) = \frac{1}{\lambda^2}\, $ |
