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  1. #1
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    definitions

    what is the difference between the joint probability density function and the joint distribution function when they are both denoted as F(x,y)?
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  2. #2
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    Quote Originally Posted by alexandrabel90 View Post
    what is the difference between the joint probability density function and the joint distribution function when they are both denoted as F(x,y)?
    The joint density is normally a lower case function like f(x,y), then:

    P((x,y) \in R)=\int_R f(x,y)\; dxdy

    The joint distribution function is usually an upper case function like F(x,y), and is defined as:

    F(x,y)=P(X<x, Y<y)=\int_{\xi=-\infty}^y \int_{\zeta=-\infty}^x f(\zeta,\xi)\; d\zeta d\xi

    CB
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