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Continuous Random Variables 10/26


\begin{displaymath}P(X\in dx,Y \in dy)=f(x,y)dxdy\end{displaymath}

The joint density is the probability per unit area near (x,y).

\begin{displaymath}P((X,Y)\in C)=\int \int_C f(x,y)dx dy\end{displaymath}

The joint density is a non-negative function that integrates to 1. Distribution Function:

\begin{displaymath}F(a,b)=\int_{-\infty}^b\int_{-\infty}^af(x,y)dxdy\end{displaymath}


\begin{displaymath}f(a,b)=\frac{\partial ^2 }{\partial a \partial b} F(a,b)\end{displaymath}



Susan Holmes
1998-12-07