Even though quantum mechanics (QM) is usually introduced as a fundamentally statistical theory it has attracted over the years a moderate attention of the scientists in the field of statistical theories, be they mathematicians or physicists. The ever lingering philosophical discussions on interpretation of QM witness a status of uncertainty of its understanding. Following the plan of our joint book with Minh-Binh Tran on “The statistical physics of non equilibrium quantum phenomena” (Springer) I shall explain first how to put the random emission of photons by an atom in an excited state into a correct statistical framework based on Kolmogorov equation for random process, based on the shortness of the duration of the emission process or “quantum jump”. In a second part I shall explain the dynamics of a typically quantum process, the condensation of atoms of a Bose gas in the ground state of lowest energy. This is explained by a finite time blow up of solutions of the Boltzmann-Nordheim kinetic equation. This blow up, contrary to some expectations, is described by a singularity of the second kind in the sense of Zeldovich. I will explain also how to describe what happens after blow-up.