이산확률변수,discrete_RV (rev. 1.3)
평균,mean:
$\displaystyle E[X]=\int_{-\infty}^{\infty}xf_X(x)dx$
분산,variance:$\displaystyle VAR[X]$
$\displaystyle =E[(X-m_X)^2]$
$\displaystyle =\int_{-\infty}^{\infty}(x-m_X)^2f_X(x)dx$
$\displaystyle =E[X^2]-E[X]^2$
$\displaystyle =\int_{-\infty}^{\infty}x^2f_X(x)dx-\left(\int_{-\infty}^{\infty}xf_X(x)dx\right)^2$
$\displaystyle =E[(X-m_X)^2]$
$\displaystyle =\int_{-\infty}^{\infty}(x-m_X)^2f_X(x)dx$
$\displaystyle =E[X^2]-E[X]^2$
$\displaystyle =\int_{-\infty}^{\infty}x^2f_X(x)dx-\left(\int_{-\infty}^{\infty}xf_X(x)dx\right)^2$