Combining measurements of time periods with unequal number of periods
Fra mn/fys/epf
Revisjon per 4. feb. 2013 kl. 18:12 av Read@uio.no (diskusjon | bidrag)
Suppose you want to estimate the mean period N measurements of the time for a number of periods per measurement ni.
We assume that each time measurement has the same uncertainty
.
We estimate the mean period by minimizing the <math>\chi^2</math> of the measurements with respect to the mean period
,
by setting the first derivative to zero:
We solve for the mean period:
To find the uncertainty on
we use the second derivative of the :
which gives us
We can estimate
from the standard deviation of the measured times with respect to the estimated mean period times the number of periods measured in measurement :These formulae give simple, well-known results for two examples:
1) All
2) All