(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

X, Y, Z random variables, independent of each other, with uniform distribution in (0,1). C = XY and R = Z^{2}. Without using the joint probability function, find P(C>R).

3. The attempt at a solution

So far:

P(C > R) = P(C - R > 0) = P(XY - Z^{2}> 0) = P(g(X,Y,Z) > 0).

Now, I don't know how to find g^{-1}(-infinity, 0) = {(x,y,z) in (0,1)^{3}: xy - z^{2}> 0} to continue to operate. Or any other way to solve this.

Any suggestions?

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# Homework Help: Random Variables Transformation

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