$\cdot$ $mean:\mu = \sum [x \cdot p(x)]$

$\cdot$ $variance:\sigma^2 = \sum [(x-\mu)^2 \cdot p(x)]= \sum[x^2 \cdot p(x)] - \mu^2$

$\cdot$ $standard\;deviation: \sigma = \sqrt{\sigma^2}= \sqrt{\sum [(x-\mu)^2 \cdot p(x)]} = \sqrt{\sum [(x^2 \cdot p(x)]- \mu^2}$

$\cdot$ maximum usual value $= \mu+2\sigma$

$\cdot$ minimum usual value $= \mu-2\sigma$