1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Statistical deviation

  1. Mar 31, 2009 #1


    User Avatar

    For some given statistics (e.g. Fermi-Dirac or Bose-Einstein), once we know the average number of particles at state r, it is easy to calculate the dispersion by calculating

    [tex]\overline{(\Delta n_r)^2} = -\frac{1}{\beta}\frac{\partial \bar{n}_r}{\partial \epsilon_r}[/tex]

    and the total number of particle is just the sum of all average number of particles.

    My question is: how do you find maximum dispersion of TOTAL NUMBER (N)?

    I know
    [tex]\overline{(\Delta N)^2} = \overline{(N-\overline{N})^2}[/tex]

    but how do you find the maximum?
  2. jcsd
  3. Apr 1, 2009 #2


    User Avatar

    For fermi stat., the total number of particles is
    [tex]N = \sum_r \overline{n}_r[/tex]

    so how to calculate [tex]\overline{N}[/tex] ?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook