  We show that the delay time distribution for wave reflection from a
one-dimensional random potential is related directly to that of the reflection
coefficient, derived with an arbitrarily small but uniform imaginary part added
to the random potential. Physically, the reflection coefficient, being
exponential in the time dwelt in the presence of the imaginary part, provides a
natural counter for it. The delay time distribution then follows
straightforwardly from our earlier results for the reflection coefficient, and
coincides with the distribution obtained recently by Texier and Comtet
[C.Texier and A. Comtet, Phys.Rev.Lett. {\bf 82}, 4220 (1999)],with all moments
infinite. Delay time distribution for a random amplifying medium is then
derived . In this case, however, all moments work out to be finite.
