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!

Homework Help: 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
    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

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook