- Events
- If , then

- Expectations
- if and are independent
- If ,

- Variance
- if and are independent
- if the are independent

- Covariance
- Mean Square Error: , more detail explanation can be found on wikipedia.
- Law of Total Expectation
- Inequalities
- Jensen: for convex ,
- Markov: If then for all ,
- Chebyshev-Cantelli: for ,
- Chebyshev’s Association: let and be nondecreasing (nonincreasing) real-valued functions defined on the real line. If is a real-valued random variable then, ()
- Harris’: extends Chebyshev’s Association to functions
- Chernoff: for all ,
- Cauchy-Schwarz: if , then
- Hoeffding’s tail: Let be independent bounded random variable such that falls in the interval with probability one. Then for any , and

- Other
- If , then with probability at least , .

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