...
The covariance of two RVs X and Y is given by:
If the Cov(X,Y) = 0, X and Y are uncorrelated.
Independence
Continuous RVs
Two jointly absolutely continuous RVs X and Y are independent if:
Or equivalently:
Discrete RVs
Two jointly discrete RVs X and Y are independent if:
Or equivalently:
Conditional Probability
Continuous RVs
Conditional PDF
...