Consider an ideal quantum gas of non-interacting identical particles in the grand canonical ensemble. The gas is in equilibrium at
temperature T and chemical potential . In the previous problem part (a) you found the number of particles ni that occupy the single-
particle energy eigenstate i is statistically independent of the number of particles nj in that occupy state j, and you found the probability
distribution pi(ni) that there are exactly ni particles in state i.
a) Using this pi(ni) rederive the average occupation number of particles in state i, for a gas of bosons and a gas of fermions.
b) Using pi(ni), derive the occupation number fluctuations - for a gas of bosons
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