Let the random point $(X,Y)$ be uniformly distributed on the unit disc $D=\{(x,y):x^{2}+y^{2}<1\}$. Show that the polar coordinates $R\in [0,1]$ and $\theta \in [0,2\pi]$ of the point are independent.
Let the random point (X,Y) be uniformly distributed on the unit disc $D=\{(x,y):x^{2}+y^{2}<1\}$
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probability-theory
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0To prove independency you need to show that $$ P\left[R=r\wedge\Theta=\theta\right]=P\left[R=r\right] P\left[\Theta=\theta\right] $$ – 2012-05-04