PDF problem

[Dreyfus]

Determine k so that
f(x,y) = kx(x-y) for 0<x<1 , -x<y<x
             0              Elsewhere
can serve as joint probability density.

I m stuck with the domain of y ......please help

[Sinistral]

here is the required domain:

[Dreyfus]

Thankx !!!

[Dreyfus]

F(x,y) is the joint cumulative distribution
I m getting joint probability density as f(x,y)= e^-(x+y) for x>0, y>0
                               0 elsewhere
Also P(X+Y>3) = 4e^-3
Please help as the answer is not matching up ?

[XIPP]

I can't understand what your citation of book says, and what do you say , I just answer this:

Determine k so that
f(x,y) = kx(x-y) for 0<x<1 , -x<y<x
             0              Elsewhere
can serve as joint probability density.

ANSWER: This is very easy problem, because you see only"0<x<1 , -x<y<x ", but if it would have been more complicated, how could you figure out the figure in minutes in the exam? Instead, just focus on the problem itself and use multiple integration as follows:

FOR THE FURTHER ANSWER, SEE THE FOLLOWING LINK:

http://cache.artofproblemsolving.com/texer/pdf/be38429dcbd2fc5e4ca53535976a52922d640fe3.pdf


Hope you have got your answer, if not, please ask!

Also, please post your book citation again, as some letters are missing there! By the way which book is that? I use DeGroot's.

[Dreyfus]

Thnkx XIPP......the ques is frm freund's mathematical stats.......nd i hv edited the original post .....hope now citations will be clear to u....