Let $X,\hspace{0.2cm}Y$ random variables with joint density $$f(x,y)=c \hspace{0.5cm} if \hspace{0.3cm} x^2+y^2 \leq 1$$ Compute $f(x|y)$
Mi problem is to cumpute $f_Y(y)$. I was trying to use polar coordinates but I'm confused at the moment to integrate ove $x$
Since $(X,Y)$ is uniformly distributed over the unit circle, $c=\frac{1}{\pi}$ and $$ f(x|y) = \frac{1}{2\pi\sqrt{1-y^2}}\cdot\mathbb{1}_{[-\sqrt{1-y^2},\sqrt{1-y^2}]}, $$ no need to use polar coordinates.