Let $Z = (X, Y)$ be a random variable uniform inside circle of radius $R$. How to find cumulative distribution function (CDF) on disk?
2026-03-30 06:27:23.1774852043
How to find CDF on disk
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Hint
See the figure below:
By the definition of the uniform distribution the CDF can be calculated as follows:
$$P(X<x,Y<y)=\frac{\text{red area(x,y)}}{R^2\pi}$$