Hi folks,

I was solving problems from the previous exams (downloaded from the SOA website). In that set of problems, I am little bit confused about Problem #112.

According to the statement of the problem,

domain for the joint density function, f(x,y) = 2(x+y), is all the region on the xy plain where f(x,y) is positive.

That means, all the region to the "right" of the line y = -x on the xy plain. But then obviously it is an open region and double integral of f(x,y) over the entire region is not going to equal 1. In that case, f(x,y) is not a density function by definition. Also, x and y have to be positive. So that leave the first quadrant to be the region but again the problem remains.

So how do you actually determine the region in that problem?

Any help would be greatly appreciated.

Thanks

I was solving problems from the previous exams (downloaded from the SOA website). In that set of problems, I am little bit confused about Problem #112.

According to the statement of the problem,

domain for the joint density function, f(x,y) = 2(x+y), is all the region on the xy plain where f(x,y) is positive.

That means, all the region to the "right" of the line y = -x on the xy plain. But then obviously it is an open region and double integral of f(x,y) over the entire region is not going to equal 1. In that case, f(x,y) is not a density function by definition. Also, x and y have to be positive. So that leave the first quadrant to be the region but again the problem remains.

So how do you actually determine the region in that problem?

Any help would be greatly appreciated.

Thanks

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