Sub:
평균,mean:
$\displaystyle E[X]=\int_{-\infty}^{\infty}xf_X(x)dx$
분산,variance:$\displaystyle VAR[X]$
$\displaystyle =E[(X-m_X)^2]$
$\displaystyle =\int_{-\infty}^{\infty}(x-m_X)^2f_X(x)dx$
$\displaystyle =E[X^2]-E[X]^2$
$\displaystyle =\int_{-\infty}^{\infty}x^2f_X(x)dx-\left(\int_{-\infty}^{\infty}xf_X(x)dx\right)^2$
from 성대 안창욱 http://kocw.net/home/search/kemView.do?kemId=444781 04_2 확률분포함수, 랜덤변수의 변환 25분$\displaystyle =E[(X-m_X)^2]$
$\displaystyle =\int_{-\infty}^{\infty}(x-m_X)^2f_X(x)dx$
$\displaystyle =E[X^2]-E[X]^2$
$\displaystyle =\int_{-\infty}^{\infty}x^2f_X(x)dx-\left(\int_{-\infty}^{\infty}xf_X(x)dx\right)^2$
