Probability Inequalities are useful for bounding quantities that might otherwise be hard to compute. A related concept is a concentration inequality, which specifically provides bounds on how far a random variable deviates from some value.

There are many useful and well studied probability/concentration inequalities including:

  • Markov's inequality
  • Chebyshev's inequality
  • Chernoff bounds
  • Hoeffding's inequality
  • Azuma's inequality

and many others.