  We study one-dimensional, continuum Bernoulli-Anderson models with general
single-site potentials and prove positivity of the Lyapunov exponent away from
a discrete set of critical energies. The proof is based on F\"urstenberg's
Theorem. The set of critical energies is described explicitly in terms of the
transmission and reflection coefficients for scattering at the single-site
potential. In examples we discuss the asymptotic behavior of generalized
eigenfunctions at critical energies.
