Re: [Phys-l] propagation of error

[Jack Uretsky <jlu@hep.anl.gov>]

For a/t, a fair approximation is given by
a(1+-d1)/t(1+-d2) = (a/t)(1+-d3)  where d3 =sqrt(d1^2 + d2^2).  Theis 
estimate agrees roughly with John's.
					Regards,
						Jack



On Tue, 5 Sep 2006, John Denker wrote:

> fizix29@aol.com wrote:
> >  Let a = 40 +/- 5 m
> >       b = 30 +/- 3 m
> >       t = 1.2 +/- 0.1 s
> >
> > What is a + b and a/t?
>
> Assuming the inputs are Gaussian and IID, then:
>
>  a+b is 70±5.8  Gaussian distributed
>
>  a/t is 33.3±4.8  nearly, but not quite Gaussian distributed
>
>
> The a+b result is easily obtained algebraically;  the uncertainties add in
> quadrature.
>  http://www.av8n.com/physics/uncertainty.htm#sec-manual-prop
>
> A fair approximation to the a/t result could also be obtained algebraically
> (hint: take logarithms) but I found it easier to just do the Monte Carlo.
>  http://www.av8n.com/physics/uncertainty.htm#sec-mg-mass
>
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