Joint PDF

정의
TBW
성질
  1. $f(x,y)\ge0$
  2. $\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}f(x,y)dxdy=1$
두 연속확률변수,continuous_random_variable $X, Y$ 가 있을 때
$1.\;\forall (x,y),\;f(x,y)\ge 0$
$2.\;\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}f(x,y)dydx=1$
$3.\;P[(x,y)\in A]=\iint_A f(x,y)dydx$
를 만족하는 $f(x,y)$ 를 결합확률밀도함수라 한다.

//tmp from http://blog.naver.com/mykepzzang/220836634095
변수가 두 개. 편미분 사용.

$f_{X,Y}(x,y)=\frac{\partial^2}{\partial x\partial y}\left[F_{X,Y}(x,y)\right]$

$P\left[x_1\le X\le x_2,y_1\le Y\le y_2\right]=F_{X,Y}(x_2,y_2)-F_{X,Y}(x_2,y_1)-F_{X,Y}(x_1,y_2)+F_{X,Y}(x_1,y_1)$

tmp from 금오공대 랜덤프로세스입문 http://kocw.net/home/search/kemView.do?kemId=1265854 확률변수3 6분

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last modified 2021-12-27 20:57:03