Finding Average <x> for Probability Densities

[z00maffect]

Homework Statement

What is the average <x> for following probability densities

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

Homework Equations

The Attempt at a Solution

dont know how to start

 

[meanyack]

use this integration
\int_{a}^{b}\left|P(x)\right|^{2}*x*dx
in the given interval [a,b]
At least, we're doing so in quantum meachanics

 

[meanyack]

I forgot to say that you must normalize this function ie
\int_{a}^{b}\left|P(x)\right|^{2}*dx=1
if the interval is not given you'll probably use [-\infty,\infty].
So that you can determine the constant "A".

 

[criz.corral]

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:

$ \int_{-\infty}^{\infty}P(x)dx = 1 $

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

$ \int_{-\infty}^{\infty}P(x)x dx $