Date: Feb 14, 2013 8:21 PM
Author: Paul
Subject: 2nd (raw?) moment of uniform PDF

I am studying a reliability paper "Analytical propagation of
uncertainties through fault trees" (Hauptmanns 2002). Unfortunately,
I cannot find an online copy to link to. The paper makes use of ye
olde uniform pdf U(a,b) [http://en.wikipedia.org/wiki/
Uniform_distribution_(continuous)]. In the process, I'm also
familiarizing myself with moments via wikipedia [http://
en.wikipedia.org/wiki/Moment_(mathematics)].

The papers states that the second moment of X~U(a,b) is:

E(X^2) = ( b^3 - a^3 ) / 3(b-a)

My own integration of x^2 from a to b yields (b^3-a^3)/3.

Can anyone point out where Hauptmanns's extra normalization factor 1/
(b-a) comes from? I thought he might have made a mistake and provided
the normalized second moment, but then the normalization factor should
be the variance, not 1/(b-a).