Generate <independent> <standard normal> variables $Z_1,Z_2$ and put $\boxed{Y=Z_1/Z_2}$. The event $Z_2=0$ has probability zero. The ratio calculation in M4 with equal <standard deviations> gives <probability density function>[density] $1/[\pi(1+y^2)]$, exactly the required $t$ distribution with one <vertex degree>[degree] of freedom. The equivalent form $Z_1/|Z_2|$ has the same law by symmetry.

Solution

Past exam of the Probability, statistics and options II course of the University of Oxford / 2010 / S / S2 / b / i / Solution

 Solution (source code)