  This article is about a problem in the numerical analysis of random
operators. We study a version of the finite section method for the approximate
solution of equations $Ax=b$ in infinitely many variables, where $A$ is a
random Jacobi operator. In other words, we approximately solve infinite second
order difference equations with stochastic coefficients by reducing the
infinite volume case to the (large) finite volume case via a particular
truncation technique. For most of the paper we consider non-selfadjoint
operators $A$ but we also comment on the self-adjoint case when simplifications
occur.
