An example of min and change of variable

Suppose \(R_1\) and \(R_2\) are two independent random variables with the same density function

\[f(x)=x\exp(-{\textstyle \frac12 }x^2)\]

for \(x\geq 0\). Find

1. the density of \(Y=\min(R_1,R_2)\);
2. the density of \(Y^2\)

[Pitman p. 336 #21]