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$x+y\leq 1$ find $Px,y(x|y)$ for solid triangle?

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    As you can tell from the answer given, it is difficult to guess what you are asking, could you please **edit** your question to state clearly what you want to know, what the **definitions** are and what you have **tried** so far.2012-12-28

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It looks as if you want the conditional density of $X$, given that $Y=y$. We can proceed from fundamental principles, or from the formula that was undoubtedly supplied to you. This formula looks like $f_X(x|Y=y)=\frac{f_{X,Y}(x,y)}{f_Y(y)}.$

The joint density $f_{X,Y}(x,y)$ is $2$ inside the triangle bounded by the axes and the line $x+y=0$, and $0$ elsewhere.

For $f_Y(y)$, we "integrate out" $x$ in the joint density function. For $0\lt y\lt 1$, we have $f_Y(y)=\int_{x=0}^{1-y} 2\,dx=2(1-y).$

Now you have the ingredients needed to write down the conditional density function.