Let f(x,y) = 6(1-y) where 0 < x < y < 1 be a possible joint distribution.
Demonstrate that this is a viable distribution (show your work)
The 0 < x < y < 1 is throwing me off. What domains should I be using when integrating with respect to x and with respect to y?

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- chestercat

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- anonymous

I've tried 0 to y for x and x to 1 for y, but I am unsure of this answer. To prove a viable distribution, I need to show that the volume of f(x,y) with respect to x and y is equal to one. I need a definite integral to equal 1.

- IrishBoy123

the volume of f(x,y) with respect to x and y is the double integral of f(x,y). and your f(x,y) is the plane \(0x + 6y +z = 6\)
your limit \(0

- IrishBoy123

notice the order of integration.

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- anonymous

Wow. You are the best. I've integrated and received the correct answer of 1. I'm ecstatic. Thanks!

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