If we have 2 independent random variables$$U, V \sim N(0,1)$$ then what is the distirbution of $U/V$ ?
My effort so far (maybe there is an easier way):
$$F_{U/V}(t) = \int_{-\infty}^{\infty}\int_{-\infty}^{tv}f_{u,v}(u,v)dudv=
\int_{-\infty}^{\infty}f_v(v)\int_{-\infty}^{tv}f_u(u)dudv=\int_{-\infty}^{\infty}\Big(\frac{1}{\sqrt{2\pi}}e^{-v^2/2} \int_{-\infty}^{tv}\frac{1}{\sqrt{2\pi}}e^{-u^2/2}du \Big)dv$$
Now I am not sure how to continue .
(I did some computations and reached that it is 0 )
