  We obtain for the first time the expressions for the mean and the variance of
the transmission coefficient for an Anderson chain in the weak localization
regime, using exact expansions of the complex transmission- and reflection
coefficients to fourth order in the weakly disordered site energies. These
results confirm the validity of single-parameter scaling theory in a domain
where the higher transmission cumulants may be neglected. We compare our
results with earlier results for transmission cumulants in the weak
localization domain based on the phase randomization hypothesis.
