Energy of the finite-volume ground state of a random Schroedinger operator is studied in the limit as the volume increases. We relate its fluctuations to a classical probability problem---extreme statistics of IID random variables---and describe the detailed behavior of its distribution. Surprisingly, the distributions do not converge---presence of two scales in the system leads to a chaotic volume dependence. A possible application to a sharp estimate of the Lifshits tail will be mentioned. The work presented is done jointly with Michael Bishop.