If two pairs of random variables $(X,Y)$ and $(U,V)$ have the same joint pdf $f_{X,Y}(x,y)=f_{U,V}(x,y)$, can we conclude that $(X,Y)=(U,V)$?
Does joint pdf uniquely describes the random variables?
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probability-distributions
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1You can conclude that the are identically *distributed*, which is not quite the same as saying they are *identical*. – 2012-04-22