Cheat3 ECE302Fall2008sanghavi - Rhea

Covariance

• $ COV(X,Y)=E[(X-E[X])(Y-E[Y])]\! $
• $ COV(X,Y)=E[XY]-E[X]E[Y]\! $

Correlation Coefficient

$ \rho(X,Y)= \frac {cov(X,Y)}{\sqrt{var(X)} \sqrt{var(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 \geq a) \leq E[X]/a\! $

for all a > 0

Chebyshev Inequality

"Any RV is likely to be close to its mean"

$ \Pr(\left|X-E[X]\right|\geq \alpha)\leq\frac{var(X)}{\alpha^2}. $

ML Estimation Rule

MAP Estimation Rule

Bias of an Estimator, and Unbiased estimators

Confidence Intervals, and how to get them via Chebyshev