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here are the properties of the joint density function, can someone explain me the 4° point? (it says: for every... as a point of continuity of f)

joint density function property

user2993157
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  • It's been three years. Are you able to prove the fourth point? I would really appreciate if you could post an answer to your own question – Emilio Dec 21 '16 at 04:10

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In a simpler one-dimension case, we have: $$ f(x)=\frac{dF(x)}{dx} $$ and in the contrary, the integral: $$ F(x)=\int_{-\infty}^x f(x)dx $$ We call $f(x)$ the probability density function(PDF), and $F(x)$ the cumulative density function(CDF). $f(x)$ denotes the probability density on the point x, $F(x)$ denotes the integral of probability density from $-\infty$ to the point x.

robit
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