**1 Cauchy-Schwartz Inequality & Jensen's Inequality**

These two inequalities are widely applied in lots of areas not only probability. For probability, they can be written as follow: **(1) Cauchy-Schwartz Inequality**, if and have finite variances, then

**(2) Jensen's Inequality**: If is a convex function, then

**2 Markov Inequalities **

Markov's inequality is pretty famous and basic, so firstly recall this inequality as follow: For any random variable and any positive function for :