Date: Nov 13, 2012 4:18 PM
Author: paulvonhippel at yahoo
Subject: CV of square

Suppose T is a random nonnegative variable with finite mean and variance, and suppose S=Sqrt(T).

Is there a useful rule of thumb, even approximate, relating the coefficient of variation (CV) of T to the CV of S? For example, if CV(S)=1/10, what does that suggest about CV(T)?

Reminder: the definition of CV is
CV(T) = Sqrt(V(T)) / E(T)
CV(S) = Sqrt(V(S)) / E(S)