This is standard and fully, correct (best) method for combining
results from several independent experiments. It is in fact used
(because it's easy conceptually and for computer) even when it's
inapplicable (e.g., if there are correlations between supposed
``independent'' random variables or if the basic experiments have too
few events to be Gaussian).
The problem is: Given N experimental measurements and
errors plus estimates of the which are
functions of N theoretical parameters. Then the probability of each
observation is
and
errors 
plus estimates 
of the 
which are
functions of N theoretical parameters. Then the probability of each
observation is
