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1. The problem statement, all variables and given/known data
"Find ##P(Y^2>4xz)##, where ##(x,y,z)\in (0,1)^3##."
2. Relevant equations
3. The attempt at a solution
##P(Y^2>4xz)=P(Y>2\sqrt{xz})+P(Y<2\sqrt{xz})=P(Y>2\sqrt{xz})=P(1>Y>2\sqrt{xz})##
Here, I set the boundaries for integration over this "wedge", for the lack of a better term.
##2\sqrt{xz}\leq y < 1##
##\frac{1}{4z}\leq x < ...##
I tried drawing a picture, but all I got from the information was that x could not be bounded by 0 or 1. The curve doesn't touch the any of the axes except at the origin.
"Find ##P(Y^2>4xz)##, where ##(x,y,z)\in (0,1)^3##."
2. Relevant equations
3. The attempt at a solution
##P(Y^2>4xz)=P(Y>2\sqrt{xz})+P(Y<2\sqrt{xz})=P(Y>2\sqrt{xz})=P(1>Y>2\sqrt{xz})##
Here, I set the boundaries for integration over this "wedge", for the lack of a better term.
##2\sqrt{xz}\leq y < 1##
##\frac{1}{4z}\leq x < ...##
I tried drawing a picture, but all I got from the information was that x could not be bounded by 0 or 1. The curve doesn't touch the any of the axes except at the origin.
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