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Homework Help: Mean, squared mean and standard deviations of a gaussian

  1. Jan 30, 2010 #1
    1. The problem statement, all variables and given/known data
    find <x>, <[tex]x^{2}[/tex]> and [tex]\sigma[/tex] of the probability distribution;
    [tex]\rho(x)[/tex] = [tex]\sqrt{\frac{\lambda}{\pi}}e[/tex][tex]^{-\lambda(x-a)^{2}}[/tex]

    2. Relevant equations

    As shown above

    3. The attempt at a solution

    I know that I can simply take the mean value (a) and the standard deviation(1/2[tex]\sigma[/tex]) from the fact that this equation is a gaussian, however wanted to know if there was a more rigorous method of calculating these figures than just saying what it is from the gaussian distribution.
  2. jcsd
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