(New page: ==Covariance, Correlation Coefficient== * <math>COV(X,Y)=E[(X-E[X])(Y-E[Y])]\!</math> * <math>COV(X,Y)=E[XY]-E[X]E[Y]\!</math>) |
(→Covariance, Correlation Coefficient) |
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* <math>COV(X,Y)=E[(X-E[X])(Y-E[Y])]\!</math> | * <math>COV(X,Y)=E[(X-E[X])(Y-E[Y])]\!</math> | ||
* <math>COV(X,Y)=E[XY]-E[X]E[Y]\!</math> | * <math>COV(X,Y)=E[XY]-E[X]E[Y]\!</math> | ||
| + | |||
| + | ==Markov Inequality== | ||
| + | Loosely speaking: In a nonnegative RV has a small mean, then the probability that it takes a large value must also be small. | ||
| + | * <math>P(X \leq a) \leq E[X]/a\!</math> | ||
| + | for all a > 0 | ||
Revision as of 07:13, 18 November 2008
Covariance, Correlation Coefficient
- $ COV(X,Y)=E[(X-E[X])(Y-E[Y])]\! $
- $ COV(X,Y)=E[XY]-E[X]E[Y]\! $
Markov Inequality
Loosely speaking: In a nonnegative RV has a small mean, then the probability that it takes a large value must also be small.
- $ P(X \leq a) \leq E[X]/a\! $
for all a > 0
