Let $Z = (X, Y)$ be a random variable uniform inside circle of radius $R$. How to find cumulative distribution function (CDF) on disk?

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    $\begingroup$ Self-duplicate of math.stackexchange.com/q/1931107 Please stop that. $\endgroup$ – Did Sep 27 '16 at 11:56
  • $\begingroup$ I reopened because the question was closed and I modified completely,but don't reopened. $\endgroup$ – Wagner Jorge Sep 27 '16 at 16:21
  • $\begingroup$ Yes, and this is called cheating the system, so: Please stop. $\endgroup$ – Did Sep 27 '16 at 18:40
  • $\begingroup$ I don't had knowledge, sorry. Please delete the question. I don't have the intention of to use cheat of system. I repeat I don't had knowledge. You can delete this question. Thank you for your help. $\endgroup$ – Wagner Jorge Sep 27 '16 at 20:03


See the figure below:

enter image description here

By the definition of the uniform distribution the CDF can be calculated as follows:

$$P(X<x,Y<y)=\frac{\text{red area(x,y)}}{R^2\pi}$$


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