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# Re: [Phys-l] propagation of error

Regarding Justin's question:

Let a = 40 +/- 5 m
b = 30 +/- 3 m

t = 1.2 +/- 0.1 s

What is a + b and a/t?

Justin Parke

The answer depends on the particular joint distribution for a, b, &
t. *If* the fluctuations are so sufficiently small that a leading
order in the fluctuation approximation is valid then the answer will
depend on the particular individual distributions for a, b, & t *as
well as* on their mutual correlation coefficients.

But *if* we can reasonably assume that the quantities a, b, & t are
independent (and hence uncorrelated) and *if* we are justified in
making a small relative fluctuation approximation to leading order
*then* we can estimate the quantities a + b & a/t as:

a + b = 70 +/- 6 m (6 ~= sqrt(34) = sqrt(5^2 + 3^2))

a/t = 33.3 +/- 5.0 m/s (5.0 ~= (40/1.2)*sqrt((5/40)^2 + (0.1/1.2)^2))

David Bowman