We give asymptotic estimates of the frequency of occurrences of a symbol in a random word generated by any bicomponent stochastic model. More precisely, we consider the random variable $Y_n$ representing the number of occurrences of a given symbol in a word of length $n$ generated at random; the stochastic model is defined by a rational formal series $r$ having a linear representation with two primitive components. This model includes the case when $r$ is the product or the sum of two primitive rational formal series. We obtain asymptotic evaluations for the mean value and the variance of $Y_n$ and its limit distribution.