Estimating fluctuation is useful in estimating certain properties of a thermodynamic system for example, light scattering is used to estimate certain properties of solution. In a colloidal or a polymeric solution, light scattering depends on the fluctuation of the number of particles within a small volume through which light passes.

A. To analyze this problem with either microcanonical, canonical or grand canonical partition function, which of the above partition functions would you select to analyze the fluctuation of the number of particles and why?

B. Let and 2 be the average values of the number (N) and the square of the number of particles in a system. Calculate (N ) using the partition function that you selected above.