  Let $\aip(t)$ be the Airy$_2$ process. We show that the random variable
[\sup_{t\leq\alpha}\{aip(t)-t^2}+\min{0,\alpha}^2] has the same distribution as
the one-point marginal of the Airy$_{2\to1}$ process at time $\alpha$. These
marginals form a family of distributions crossing over from the GUE Tracy-Widom
distribution $F_{\rm GUE}(x)$ for the Gaussian Unitary Ensemble of random
matrices, to a rescaled version of the GOE Tracy-Widom distribution $F_{\rm
GOE}(4^{1/3}x)$ for the Gaussian Orthogonal Ensemble. Furthermore, we show that
for every $\alpha$ the distribution has the same right tail decay
$e^{-(4/3)x^{3/2}}$.
