Let $x$ and $y$ be $2$ independent random vectors on the unit disk such that their joint density is just $\frac{1}{\pi}$. What is the probability that $x+y$ is less than $1$?
Probability of sum of two independent variables given joint density
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probability
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1I suspect you mean that $x$ and $y$ are the *coordinates* of a *point* in the unit disk? However, in that case they're not independent. If you do mean vectors, how do you compare $x+y$ to $1$? – 2012-10-26
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0Are you sure they are not independent? – 2012-10-26