  In this paper we consider the problem of efficient computation of
cross-moments of a vector random variable represented by a stochastic
context-free grammar. Two types of cross-moments are discussed. The sample
space for the first one is the set of all derivations of the context-free
grammar, and the sample space for the second one is the set of all derivations
which generate a string belonging to the language of the grammar. In the past,
this problem was widely studied, but mainly for the cross-moments of scalar
variables and up to the second order. This paper presents new algorithms for
computing the cross-moments of an arbitrary order, and the previously developed
ones are derived as special cases.
