期待値,分散,標準偏差

離散型確率変数 $X$ が確率関数 $P_{i}(i=1,2,\cdots,n)$ の確率分布に従うとき，期待値 $\mu$，分散 $V[X]$，標準偏差 $\sigma$ は以下のように定義される．\[\mu = E[X] = \sum_{i=1}^{n} x_{i}P_{i} = x_{1}P_{1}+x_{2}P_{2}+ \cdots +x_{n}P_{n}\]\[V[X] = \sum_{i}^{n}(x_{i}-\mu)^{2}P_{i}\]\[\sigma = \sqrt{V[X]}\]

Mathematics is the language with which God has written the universe.