joint pdf HELP!

anonMe

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Apr 21, 2014
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3
f(x,y)=8xy ; 0<x<1, 0<y<x

Calculate P(X<1/2,Y<1/2)

I keep getting this question wrong, and I don't know where or why I'm going wrong.

My workings;

Integrate f(x,y) in 0<x<1/2, 0<y<1/2
and I get an answer of 1/8

but that's wrong.
Would appreciate any help

Thanks
 
f(x,y)=8xy ; 0<x<1, 0<y<x
Calculate P(X<1/2,Y<1/2)
I keep getting this question wrong, and I don't know where or why I'm going wrong.

Integrate f(x,y) in 0<x<1/2, 0<y<1/2
and I get an answer of 1/8

Try \(\displaystyle \displaystyle\int_0^{0.5} {\int_0^x {8xydydx} }\)
 
To supplement pka's response, because of the "0< y< x" condition, the overall domain for this pdf is the triangle with vertices at (0, 0), (1, 0), and (1, 1), NOT the rectangle with vertices at (0, 0), (1, 0), (1, 1), and (0, 1). The condition that x and y be less than 1/2 restricts it to the triangle with vertices at (0, 0), (1/2, 0), and (1/2, 1/2). That is why the limit on the x-integration are 0 to 1/2 while the limits on the y-integration are 0 to x.
 
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