# Random Walk Problem

1. Jan 31, 2005

### Goldenlemur

Ok I have a varaition of the random problem as follows. We have a container with volume V and N particles. We consider a subvolume v and n particles. The probability of particles being inside v is (v/V)

Ok I found the mean of n (mean number of molecules in v)

< n > = N*v*(1/V)

Then they ask to find the relative dispersion in mean number of molecules in v

relative dispersion = ([1-(v/V)]/ (< n > + [1-(v/V)]))

1) Next they ask conisder relative dispersion when v << V

Well the relative dispersion then becomes,

relative dispersion = 1/< n > ; one over the mean of n

2) Then consider relative dispersion when v appoarching V

relative dispersion = 0

I am not sure what is the physical meaning of 1 and 2 so not sure if I'm doing the problem right. I think it is... I have the following reason for 2 since the subvolume is appoarcing the oringal volume of the containter then the probability of particle in v becomes one therefore the dispersion from the mean vanishes... Can some give me some guidence?