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Quantifying the statistical error in a counting experiment 
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#1
Jan2213, 03:54 AM

P: 35

I need to find the statistical error in a counting experiment. Specifically, a decay can proceed via option A or option B and I need to find the branching ratio BR_a=(N_a)/(N_a+N_b). If I were to do this counting experiment multiple times my results for BR_a would follow the binomial distribution since there are two decay channels.
How do I quantify the statistical error in my result given that I conduct the experiment only once? 


#2
Jan2213, 10:25 AM

Mentor
P: 11,917

Do you have a fixed number of decays ("I take data until I have 100 decays in those two channels")?
No => you can treat N_a and N_b as the result of independent Poisson processes. Yes => the denominator is fixed, and N_a comes from a binomial distribution. 


#3
Jan2813, 09:33 PM

Sci Advisor
HW Helper
PF Gold
P: 2,015

The usual statistical error gives N_A+  sqrt{N_A}.



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