Theoretical problem--the difference between running everage and profile in forcite

Hi everyone
I know the running everage of the potential energy can be used to judge the equilibrium state,but I do not the difference between running everage and profile of the potential energy.I have searched the Help Document,it states "the running everage represents the cumulative average of the selected property for all selected frames between the first and the current trajectory frame".I guess  the "first and the current trajectory frame" represent the frame generated at every simulation step,so if the time step is 0.10 fs and the frame out put is 1000,there will be 1000 frames( I think each frame is a point in the phase space ),and I guess "the cumulative average"  is the ensemble everage over the 1000 frames,thus the running everage of potential energy is the ensemble everage over the 1000 frames.In addition,I guess the final reported structure also is the ensemble everage stucture of the 1000 frames.My question are


(1)Whether my guess is right?
(2)Why can the running everage can be used to judge the equilibrium state?
(3)Is there any difference between running everage and profile?


I have read some books about MD,but these questions puzzle me for several weeks.Any help will be appriciated.

Sincerely
Li