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Consider the RV X with uniform distribution over [0,1]:
Suppose h(x) = x3/2:
Discrete RVs
Consider the RV X with binomial distribution and parameters N = 2 and p = 0.2. Support of X is {x0 = 0, x1 = 1, x2 = 2}.
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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
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