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
- the density of \(Y=\min(R_1,R_2)\);
- the density of \(Y^2\)
[Pitman p. 336 #21]
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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
[Pitman p. 336 #21]