$$ Suppose that $X$ and $y$ are two random variables whose joint distribution has density f_{XY)(x, y)=\left\{\begin{array}{11} \frac{2}{\pi\left(1+y^{2} ight)} & \text { if } 00 W 0 & \text { otherwise. } \end{array} ight. $$ let $u$ and $V$ be random variables satisfying $$ U=\sqrt{\frac{X}{Y}} \text { and ) V=\sqrt{XY} Select the correct statement of the density of the joint distribution of $U$ and $V$. Select one: a. $f_{U v}(u, v)=\frac [4 u v} {\pi\left(u^{2}+v^{2} ight)]$ if $u>0$, and $v>0$ b. $f_{U V}(u, v)=\frac{4 u v) {\pi\left(u^{2}+v^{2} ight)}$ if $u>0, v>0$ and $u v0, v>0$ and $u v0$ and $v>0$ f. $f_{U V}(u, v)=\frac{u^{3}} {\pi\left(U^{2}+v^{2} ight)}$ if $00, v>0$ and $u v