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# Re: [Phys-l] propagation of error

• From: Jack Uretsky <jlu@hep.anl.gov>
• Date: Tue, 5 Sep 2006 17:56:17 -0500 (CDT)

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
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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