| Inequalities | |
|---|---|
| Triangular Inequalities | |
| $ \vert a_1 \vert - \vert a_2 \vert \leqq \vert a_1 +a_2 \vert \leqq \vert a_1 \vert + \vert a_2 \vert $ | |
| $ \vert a_1 + a_2 + \cdots + a_n \vert \leqq \vert a_1 \vert + \vert a_2 \vert + \cdots + \vert a_n \vert $ | |
| Cauchy-schwarz Inequality | |
| $ \vert a_1b_1 + a_2b_2 + \cdots + a_nb_n \vert ^2 \leqq \left ( \vert a_1 \vert ^2 + \vert a_2 \vert ^2 + \cdots + \vert a_n \vert ^2 \right ) \left ( \vert b_1 \vert ^2 + \vert b_2 \vert ^2 + \cdots + \vert b_n \vert ^2 \right ) $ | |
| Gaussian random variable with parameter $ \mu \mbox{ and } \sigma^2 $ | $ \,E[X] = \mu,\ \ Var(X) = \sigma^2\, $ |
| Exponential random variable with parameter $ \lambda $ | $ \,E[X] = \frac{1}{\lambda},\ \ Var(X) = \frac{1}{\lambda^2}\, $ |
| Inequalities Involving Arithmetic, Geometric and Harmonic | |
| Holder Inequality | |
| Tchebytchev Inequality | |
| Minkowski Inequality | |
| Cauchy-schwarz Inequality for Integrals | |
| Holder Inequality for Integrals | |
| Minkowski Inequality for Integrals | |
