We consider long strips of finite width L ≤ 13 sites of ferromagnetic Ising spins with random couplings distributed according to the binary distribution: P(J_ij)= 1 2 ( δ (J_ij -J_0) + δ (J_ij -rJ_0) ) , 0 < r < 1 . Spin-spin correlation functions <σ_0σ_R> along the "infinite" direction are computed by transfer-matrix methods, at the critical temperature of the corresponding two-dimensional system, and their probability distribution is investigated. We show that, although in-sample fluctuations

more »

... do not die out as strip length is increased, averaged values converge satisfactorily. These latter are very close to the critical correlation functions of the pure Ising model, in agreement with recent Monte-Carlo simulations. A scaling approach is formulated, which provides the essential aspects of the R-- and L-- dependence of the probability distribution of <σ_0σ_R>, including the result that the appropriate scaling variable is R/L. Predictions from scaling theory are borne out by numerical data, which show the probability distribution of <σ_0σ_R> to be remarkably skewed at short distances, approaching a Gaussian only as R/L ≫ 1 .