[neutron-mc] Statistical Errors question:

[Peter Willendrup]

Hello Aaron,

On Jun 3, 2008, at 3:56 AM, Aaron M. Percival wrote:

> In section 4.2.1 of the McStas user manual makes the following  
> statement:
>
> "...we observe a large number of neutrons, N >= 10. Then N almost  
> follows a normal distribution with the uncertainty sigma(N) =  
> sqrt(N')."
>
> Here N is the number of neutron counts in a particular bin of a  
> monitor.
>
> I was wondering why mathematically this is true.  Is it an  
> application of the Central Limit Theorem?

Probably true. In case you want a more formal proof of this, see for  
instance Byron P. Roe "Probability and Statistics in Experimental  
Physics",
  ISBN 0-387-97849-6, Springer Verlag, pp. 35-37. (Or likely any other  
standard book on the topic.)

Cheers,

Peter