Expectation value of the expectation value

[jinksys]

Homework Statement

The expectation value of the position observable x is <x> = ∫ψ*xψdx. The expectation value of the expectation value, <<x>>=<x>, is still the expectation value...why?

Homework Equations

The Attempt at a Solution

All I can think of is that the expectation value is essentially an average, and the average of an average is the original average.

i.e.) A={2,8} The average is (2+8)/2 = {5}
The average of {5} = {5}.

 

[dextercioby]

The expectation value is a number which <comes out> of the integral of the expectation value of the the expectation value.