  The center of gravity is a widespread algorithm for position reconstruction
in particle physics. For track fitting, its standard use is always accompanied
by an easy guess for the probability distribution of the positioning errors.
This is an incorrect assumption that degrades the results of the fit. The
explicit error forms show evident Cauchy-(Agnesi) tails that render problematic
the use of variance minimizations. Here, we report the probability
distributions for some combinations of random variables, impossible to find in
literature, but essential for track fitting: $x={\xi}/{(\xi+\eta)}$,
$y={(\xi-\eta)}/[2{(\xi+\eta)}]$, $w=\xi/\eta$, $x=\theta(x_3-x_1)
(-x_3)/(x_3+x_2) +\theta(x_1-x_3)x_1/(x_1+x_2)$ and
$x=(x_1-x_3)/(x_1+x_2+x_3)$. The first three are directly connected to each
other and are partial forms of the two-strip center of gravity. The fourth is
the complete two-strip center of gravity. For its very complex form, it allows
only approximate expressions of the probability. The last expression is a
simplified form of the three-strip center of gravity. General integral forms
are obtained for all of them. Detailed analytical expressions are calculated
assuming $\xi$, $\eta$, $x_1$, $x_2$ and $x_3$ independent random variables
with Gaussian probability distributions (the standard assumption for the strip
noise).
