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Random Walk Problem

  1. Jan 31, 2005 #1
    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?
  2. jcsd
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