Can someone describe why this is true? I have no idea what steps to take to get this answer.

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- Mar 11th 2010, 05:49 PMgarymarkhovDouble integration problem

Can someone describe why this is true? I have no idea what steps to take to get this answer. - Mar 11th 2010, 06:01 PMTKHunny
It's a joke, right? Maybe the 8 was bent over in the original statement, " "?

That region is very much unbounded. You will be hard-pressed to drag a finite solution from it. - Mar 11th 2010, 06:20 PMgarymarkhov
- Mar 11th 2010, 08:56 PMTKHunny
This shows us the value of presenting the actual problem statement. The limits make all the difference.

means in the x-direction. It is no longer unbounded.

Please evaluate the iterated integral with these very useful finite limits.

For P(X + Y < 3), notice that this is nicely related to P(X < 3 - Y) and you should be almost done. - Mar 11th 2010, 10:09 PMdrumist
To clarify, your notation is bad.

Consider for a moment a simpler function:

If you are asked to evaluate this integral:

then you would have to split it into separate regions because it's a piecewise function, i.e.,

Naturally, the integrals on the sides equal zero, so we just write it as

Extending this logic into two variables with your problem shows that you should be evaluating this:

- Mar 12th 2010, 06:08 AMgarymarkhov
- Mar 12th 2010, 02:37 PMTKHunny
It might be easier to worry about P(Y < 3 - X). You have new limits. Your Y-limits are no longer all of (2,4). You might get (2,3-X)? Since x runs in (0,2), that seems quite reasonable.

- Mar 14th 2010, 06:46 PMgarymarkhov
- Mar 14th 2010, 11:14 PMdrumist
Close, but you made a mistake with the limits of integration.

Graph the region that the density is defined on. Then plot the line x+y=3. You will then be able to identify the region corresponding with x+y<3. You should integrate the joint density over this region only.

Can you identify your error? - Mar 16th 2010, 01:48 PMgarymarkhov
- Mar 17th 2010, 11:24 PMdrumist
Sorry for taking so long to respond.

The region you displayed is correct! However, your endpoints are still not correct. :\

This is the correct setup:

The error you originally made was that you took y from 2 to 4, but the region goes from 2 to 3.