Suppose that $X$ and $Y$ are independent variables of distribution $N(0,1)$, and $Z=\min(X,Y)$. Show that $Z^2 ∼ χ^2 (1)$
If $X$ and $Y$ are independent random variables, with $Z = \min(X,Y),$ prove that $Z^2\sim\chi^2(1),$