
$$f\left(x\right)=\frac{\left(\frac{\nu 1}{2}\right)!}{\left(\frac{1}{2}\nu 1\right)!\sqrt{\pi \nu}{\left(1+\frac{{x}^{2}}{\nu}\right)}^{\frac{1}{2}\left(\nu +1\right)}}\text{.}$$ 
$${y}_{i}\sqrt{\frac{\nu}{{z}_{i}}}\text{, \hspace{1em}}i=1,\dots ,n$$ 