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Joint Distribution help please


New member
Apr 19, 2012
Can't get my head around this joint distribution problem.

Suppose X and Y have joint distribution given by:

\(\displaystyle f(x,y) = \left\{
\begin{array}{l l}
x+y & \quad \text{if 0 $\leq x, y $\leq 1}\\
0 & \quad \text{otherwise}\\
\end{array} \right.\)

Find the distribution of X+Y

Having difficulties finding the boundaries for my integration. I know that I need do declare a dummy variable t = X + Y
Been stuck on this for a few hours now, help is much appreciated! Thanks.
Last edited:


Staff member
Apr 12, 2005
The fact that you used the singular, "integration", is not encouraging.

You must chop your coordinate plane up in to various regions and perform integration against all of them - in this case, 5.

1) Create a coordiate plane, x,y.
2) Draw in the lines x = 0, x = 1, y = 0, y = 1
3) Stare at it until you see the five important regions.

Hint1: Quadrants II, III, and IV are zero.
Hint2: For x > 1 AND y > 1, it's all unity (1).

Okay, now you find the other three regions.