= Solution
The first right endpoint is the smallest of $n$ <independent> pair maxima. A maximum exceeds $r$ with <probability> $1-r^2$, so for $0\le x\le\sqrt n$,
$$
\Pr(R_1\ge x/\sqrt n)=\left(1-\frac{x^2}{n}\right)^n.
$$
Taking the limit gives the requested, correctly normalized result
$$
\boxed{\Pr(\sqrt nR_1\ge x)\longrightarrow e^{-x^2}\quad(x>0).}
$$
Thus $\sqrt nR_1$ converges to a continuous nonnegative limit $W$ with survival function $\Pr(W\ge x)=e^{-x^2}$. In particular the scaled first right endpoint is tight. This calculation uses maxima of pairs, not the first <order statistic> of all $2n$ individual endpoints, which would have a different scale. The converted TeX loses the formula in this part; the displayed limit has been recovered directly from the PDF.
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