Consider a quantum state of energy $E$, which can be occupied by any number $n$ of some bosonic particles, including $n=0$. At absolute temperature $T$, the probability of finding $n$ particles in the state is given by $P_{n}=N \exp \left(-n E / k_{\mathrm{B}} T\right)$, where $k_{\mathrm{B}}$ is Boltzmann's constant and the normalization factor $N$ is determined by the requirement that all the probabilities sum to unity. Calculate the mean or expected value of $n$, that is, the occupancy, of this state, given this probability distribution.
