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Independence for Continuous Random Variables 10/27

We no longer have individual mass distribution functions which are non-zero, so we use the densities:

\begin{displaymath}X\; and \; Y are\; independent\; iff\; f(x,y)=f_X(x)f_Y(y)\end{displaymath}

which is also equivalent to the products of the distribution functions being equal to the joint distribution function:

\begin{displaymath}X\; and \; Y are\; independent\; iff\; F(x,y)=F_X(x)F_Y(y)\end{displaymath}

Susan Holmes