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Let $(X,Y,Z)$ be a continuous random vector with joint density $$ f_{(X,Y,Z)}(x,y,z) = 6e^{-x-y-z},\quad 0 < x < y < z. $$

What is the marginal density of $X,Y$ and $Z$?

I have calculated $f_X(x)$ here. I have calculated $f_Y(y)$ here. I have calculated $f_Z(z)$ here.

Is this right?

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What kind of comprehension do you try to achieve by plugging these into W|A? If your test is Plug these into W|A and write down the result, OK. Otherwise, I fail to see the point. (Strictly speaking, note that you have calculated nothing, W|A has.) – Did Sep 24 '12 at 11:33
I'm using Wolfram Alpha because I'm not familiar with writing formatted mathematical notation. The computation is easy; I'm more concerned with whether I set up the boundaries of the integrals correctly. – idealistikz Sep 24 '12 at 19:54
up vote 0 down vote accepted

Those are correct, I suggest you integrate on your own(pencil and paper) since you will be doing so for your tests.

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I did, but I posted the links to Wolfram because I am unfamiliar with writing mathematical notation on this site. – idealistikz Sep 24 '12 at 10:58

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