# Mean Square Deviations of density - need clarification please

1. Nov 13, 2008

### EvilLost

I am very lost when expectation values meet DENSITY.

I know the following:
<X> = sum[X*prob(X)]
<(dX)^2>=<X^2>-<X>^2

I am COMPLETELY lost on how to find the "value" X and its "probability" P(X) in situations dealing with DENSITY.

This might be best described by an example:

Given: (e-1)/(e+2)=Ap e=dielectric constant; A=constant; p=DENSITY

Show that the fluctuations in dielectric constant of a small quantity of N moles of matter in a large system are:

<(de)^2>= [kT(kappa) *(e-1)^2 * (e+2)^2 ] / 9V where V is avg volume

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In short....where do I even begin to calculate <e> or <e^2>?? I fail to understand how this problem even relates to the expectation value...

An expectation value is found by taking the value at a given point, times its probability right? (Sum of[X*P(X)] where P(X) is the probability that X will happen). How does this relate in any way to the given problem??

Am I mistaken in my understanding or can anyone at least point me in the slightest of directions? 5 hours later and nothing to show for it is incredibly frustrating.