"The probability that a system in the grand canonical ensemble has exactly N particles is given by
p(N)=Z(z,V,T)zNQN(V,T)."
Verify this statement and show that in the case of a classical, ideal gas the distribution of particles among the members of a grand canonical ensemble is identically a Poisson distribution. Calculate the root-mean-square value of (ΔN) for this system both from the general formula (4.5.3) and from the Poisson distribution, and show that the two results are the same.