결합확률밀도함수,joint_probability_density_function,joint_PDF

Joint PDF

정의
TBW

성질

$f(x,y)\ge0$
$\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}f(x,y)dxdy=1$

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

links ko ¶

https://blastic.tistory.com/210

Compare:

다른 결합 함수:

결합확률질량함수,joint_probability_mass_function,joint_PMF
결합누적분포함수,joint_cumulative_distribution_function,joint_CDF

다른 밀도함수:

조건부확률밀도함수,conditional_probability_density_function,conditional_PDF
주변확률밀도함수,marginal_probability_density_function,marginal_PDF

[https]

수학백과: 결합확률밀도함수
https://mathworld.wolfram.com/JointDistributionFunction.html

Up:

결합확률분포,joint_probability_distribution
확률밀도함수,probability_density_function,PDF