Dear Giuseppe,
Thank you very much for these clarifications:). Your points 1 & 2 clearly explains my doubt and exactly what I needed.
To address your point 3, why I used the average (weighted uncertainty from the *tab.lis file,
I’m more interested in the overall reduction of the error bars when I plot the differential spectrum.
For example, Suppose that I have 1024 bins, how do I chose a single bin to judge the statistical accuracy of the overall result? Also, Since these errors are themselves random, I think that a single (randomly chosen bin) could present a large error (due to low counts in that bin) whereas the other bins will have lower errors. Correct?
This is why I multiplied every bin error with the corresponding counts (3rd column) x (4th column) computed the weighted average as shown in my formula.
This value thus decreases with the number of contributions N as 1/sqrt(N) N but I wasn’t sure why the relation N_2 /N_1 = (sigma1/sigm2)^2 was not being respected.
So, based on your explanation and notes from slide 30 of the presentation, I do not except N_2 /N_1 = (sigma1/sigm2)^2 to be exact except for very large N (–> infinity) where the calculated mean converges to the true values. Correct?
I will also love for you to check this query (Uncertainty, Average Energy, USRBIN and DETECT Cards - #5 by zavier.ndum.ndum) and will be grateful for y’alls’ clarification.
Sincerely
Zavier