 
Summary: Fluctuations
The number density is the number of molecules per
unit volume of gas. We can find the number density
from the ideal gas law. For example, the number
density of air in this classroom is about 2.7E25 1/m3
(for p=101.3kPa, T=288 K).
Let's draw a volume of 1 cubic meter somewhere in
the classroom. The number of molecules in it will
vary at any given moment of time because
molecules go in and out of the volume. Number
density is the average value of a random variable X
equal to the number of molecules in 1 m3
volume.
We'll derive the distribution function for X or, in other
words, we will find how X fluctuates about an
average n.
Suppose we have N molecules distributed
