On 24 Mar 1998 16:18:23 "James W. Wheeler" <jwheeler@eagle.lhup.edu> wrote:
The error in the result of A-B should be sqrt(145+41), which is 13.6.
It is prediction for the Geiger Tube counting, where A=145 is the number
of counts per minute with the background and B=41 is the background
counts per minutes. A and B were measured only once; what is the expected
distribution of C=A-B for a large number of experiments?
In order to verify this prediction (distribution of C should be Gaussian,
centered on 145-41=104, whose standard deviation is 13.6) I simulated
100,000 experiment with a program based on random numbers. The result
of this brute force approach confirmed the prediction very well.
I am no longer puzzled by the fact that the error in A is 8.2%, the error
in B is 15.6% while the error in A-B is only 13%. The error in B can be
as large as 100% but this will have a minimal effect on the error in C
if B<<A. In this case A is more that three times larger than B. I do not
know why this was not obvious to me before.