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*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

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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**References**:**[Phys-l] propagation of error***From:*fizix29@aol.com

**Re: [Phys-l] propagation of error***From:*John Denker <jsd@av8n.com>

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