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- Jan 26, 2012

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**Problem**: A point is uniformly distributed within the disk of radius 1. That is, its density is\[f(x,y)=C,\qquad 0\leq x^2+y^2\leq 1\]

Find the probability that its distance from the origin is less than $x$, $0\leq x\leq 1$.

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**Note**: $f(x,y)$ is a density function if $\displaystyle\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} f(x,y)\,dy\,dx = 1$.

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