Finding marginal distributions when the domain is non-rectangular?
Hi all.
I have a joint continuous p.d.f. of random variables X and Y, specified over 0 < x < y < infinity. Graphically speaking, this domain is not rectangular. The first part of the question asked me to find the normalising constant of the p.d.f. I was given, which I did by integrating over the whole rectangular region and halving (the p.d.f. was symmetric in x and y, which is what I used to justify this). Now my question is: how do I get at the marginal distributions? I know normally you would integrate one of the variables out over the whole range but does the shape of my domain affect this?
I have a joint continuous p.d.f. of random variables X and Y, specified over 0 < x < y < infinity. Graphically speaking, this domain is not rectangular. The first part of the question asked me to find the normalising constant of the p.d.f. I was given, which I did by integrating over the whole rectangular region and halving (the p.d.f. was symmetric in x and y, which is what I used to justify this). Now my question is: how do I get at the marginal distributions? I know normally you would integrate one of the variables out over the whole range but does the shape of my domain affect this?
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