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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
Uniform random variable over (a,b) $ \,E[X] = \frac{a+b}{2},\ \ Var(X) = \frac{(b-a)^2}{12}\, $
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

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