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| − | ==Covariance | + | ==Covariance== |
* <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> | ||
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| + | ==Correlation Coefficient== | ||
==Markov Inequality== | ==Markov Inequality== | ||
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* <math>P(X \geq a) \leq E[X]/a\!</math> | * <math>P(X \geq a) \leq E[X]/a\!</math> | ||
for all a > 0 | for all a > 0 | ||
| + | |||
| + | ==Chebyshev Inequality== | ||
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| + | ==ML Estimation Rule== | ||
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| + | ==MAP Estimation Rule== | ||
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| + | ==Bias of an Estimator, and Unbiased estimators== | ||
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| + | ==Confidence Intervals, and how to get them via Chebyshev== | ||
Revision as of 15:49, 18 November 2008
Contents
Covariance
- $ COV(X,Y)=E[(X-E[X])(Y-E[Y])]\! $
- $ COV(X,Y)=E[XY]-E[X]E[Y]\! $
Correlation Coefficient
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 \geq a) \leq E[X]/a\! $
for all a > 0
