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Finding average <x>

  1. Oct 31, 2009 #1
    1. The problem statement, all variables and given/known data

    What is the average <x> for following probability densities

    P(x) = A[a[tex]^{4}+(x-x_{0})^{4})]^{-1}[/tex]


    2. Relevant equations



    3. The attempt at a solution

    dont know how to start
     
  2. jcsd
  3. Oct 31, 2009 #2
    use this integration
    [tex]\int_{a}^{b}\left|P(x)\right|^{2}*x*dx[/tex]
    in the given interval [a,b]
    At least, we're doing so in quantum meachanics
     
  4. Oct 31, 2009 #3
    I forgot to say that you must normalize this function ie
    [tex] \int_{a}^{b}\left|P(x)\right|^{2}*dx=1 [/tex]
    if the interval is not given you'll probably use [tex][-\infty,\infty][/tex].
    So that you can determine the constant "A".
     
  5. Nov 2, 2009 #4
    Hi!

    I think you don't need to take the square of P(x) because he's already probability density.

    You normalize the probability density to find A:

    [tex]$ \int_{-\infty}^{\infty}P(x)dx = 1 $ [/tex]

    And then, the mean value of x ( <x> ) is:

    [tex]$ \int_{-\infty}^{\infty}P(x)x dx $ [/tex]
     
    Last edited: Nov 3, 2009
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