標本確率変数(Specimen random variable) / 標本確率変数の期待値と分散

$$\begin{array}{rcl}\mathrm{母}\mathrm{集}\mathrm{団}\mathrm{の}\mathrm{確}\mathrm{率}\mathrm{変}\mathrm{数}& :& X\\ \mathrm{標}\mathrm{本}\mathrm{確}\mathrm{率}\mathrm{変}\mathrm{数}& :& X_k(k=1,2,\dots ,n)\end{array}$$ $$\begin{array}{rcl}\mu & =& E[X]\\ {\sigma }^2& =& V[X]\end{array}$$ 標本確率変数$X_k$は母集団の確率変数$X$と同じ確率分布(母集団)に従うので，$X_k$の期待値・分散は$X$の期待値・分散と等しい． $$\begin{array}{rclcl}E[X_k]& =& E[X]& =& \mu \\ V[X_k]& =& V[X]& =& {\sigma }^2\end{array}$$