  Statistical properties of the transmittance ($T$) and reflectance ($R$) of an
amplifying layer with one-dimensional disorder are investigated analytically.
Whereas the transmittance at typical realizations decreases exponentially with
the layer thickness $L$ just as it does in absorbing media, the average
$\left\langle T\right\rangle $ and $\left\langle R\right\rangle $\ are shown to
be infinite even for finite $L$ due to the contribution of low-probable
resonant realizations corresponding to the non-Gaussian tail of the
distribution of $\ln T$. This tail differs drastically from that in the case of
absorption. The physical meaning of typical and resonant realizations is
discussed.
