| Line 3: | Line 3: | ||
! style="background: rgb(228, 188, 126) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; font-size: 110%;" colspan="2" | Inequalities | ! style="background: rgb(228, 188, 126) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; font-size: 110%;" colspan="2" | Inequalities | ||
|- | |- | ||
| − | ! 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" | | + | ! 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" | Triangular Inequalities |
|- | |- | ||
| align="right" style="padding-right: 1em;" | The complement of an event A (i.e. the event A not occurring) | | align="right" style="padding-right: 1em;" | The complement of an event A (i.e. the event A not occurring) | ||
| Line 18: | Line 18: | ||
| align="right" style="padding-right: 1em;" | Exponential random variable with parameter <math>\lambda</math> | | align="right" style="padding-right: 1em;" | Exponential random variable with parameter <math>\lambda</math> | ||
| <math>\,E[X] = \frac{1}{\lambda},\ \ Var(X) = \frac{1}{\lambda^2}\,</math> | | <math>\,E[X] = \frac{1}{\lambda},\ \ Var(X) = \frac{1}{\lambda^2}\,</math> | ||
| + | |- | ||
| + | ! 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" | Inequalities Involving Arithmetic, Geometric and Harmonic | ||
| + | |||
| + | |- | ||
| + | ! 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" | Holder 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" | Tchebytchev 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" | Minkowski 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 for Integrals | ||
| + | |- | ||
| + | ! 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" | Holder Inequality for Integrals | ||
| + | |- | ||
| + | ! 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" | Minkowski Inequality for Integrals | ||
| + | |- | ||
|} | |} | ||
Revision as of 14:15, 24 November 2010
| Inequalities | |
|---|---|
| Triangular 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}\, $ |
| Inequalities Involving Arithmetic, Geometric and Harmonic | |
| Holder Inequality | |
| Tchebytchev Inequality | |
| Minkowski Inequality | |
| Cauchy-schwarz Inequality for Integrals | |
| Holder Inequality for Integrals | |
| Minkowski Inequality for Integrals | |
