Show that the $t$ -distribution with $r=1$ degree of freedom and the Cauchy distribution are the same.
Added by -Ngel L.
Step 1
Recall the probability density function (pdf) of the $t$-distribution with $r$ degrees of freedom: $$ f(t) = \frac{\Gamma(\frac{r+1}{2})}{\sqrt{r\pi}\Gamma(\frac{r}{2})}\left(1+\frac{t^2}{r}\right)^{-\frac{r+1}{2}} $$ Show more…
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