Re: [Phys-l] propagation of error

[John Denker <jsd@av8n.com>]

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