'''Joint PDF'''

정의
TBW
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성질
 1. $f(x,y)\ge0$
 1. $\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}f(x,y)dxdy=1$
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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 '''결합확률밀도함수'''라 한다. 
 
//tmp from http://blog.naver.com/mykepzzang/220836634095
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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

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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]]

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[[https://terms.naver.com/entry.naver?docId=3404948&cid=47324&categoryId=47324 수학백과: 결합확률밀도함수]]
https://mathworld.wolfram.com/JointDistributionFunction.html

Up:
 [[결합확률분포,joint_probability_distribution]]
 [[확률밀도함수,probability_density_function,PDF]]