4.1 Canonical phase space density:
Considering the Maxwell-Boltzmann distribution in a classical
3D fluid, show that
a) with increasing kinetic energy the density of states decreases
as
;
b) in spite of this the most probable kinetic energy is not zero.
Apply this to the general canonical phase space.

4.2 Grand canonical ensemble:
Using the grand partition function, derive the mean number of particles
in one of an ideal gas at standard conditions.