Remarks on Counting Errors in Moments---I

• In formula

  

• I used to worry if you should include counting error in N in error estimate which otherwise only involves the Standard Deviation of f.
• If N is a priori fixed, clearly there is no error but suppose the events used in Equation (26) are those that fall in a particular subregion (counter) of a bigger sample space (and is defined only over this subregion).
• Then the estimate of probability of falling into counter certainly involves error! What about the mean of a quantity within subregion---does this involve this error?
• The problem is: what is error in a moment: should it include counting error?
• The answer is no---one uses identical formulae in case where number of events prescribed and not subject to counting error.