Monochromatic plane-wave illumination of a randomly stratified, laterally homogeneous sediment layer is considered. The deposition process creating the stochastic layering is assumed to be a continuous parameter, finite state Markov chain. A Riccati equation for the plane-wave reflection coefficient is formulated and first-order partial differential equations for relevant probability density functions are subsequently obtained. These equations are solved numerically for a two-material turbidite model similar to the one considered by Gilbert [J. Acoust. Soc. Am. 68, 1454-1458 (1980)]. Statistical moments of the reflection coefficient are computed at 25 and 250 Hz as a function of overall sediment thickness. These equations are also used to derive the nonrandom or "smooth" geoacoustic model that is appropriate in the low-frequency limit.