A nonsecular procedure is derived for modifying the intensity distributionI(μ) computed in a channel with a sound speed profile μ, so as to account for small changes Δμ in the profile. This procedure is then employed to relate the statistics of a random ensemble of profiles to the statistics of the corresponding intensity distributions. The difference betweenI(〈μ〉), the intensity distribution for the mean (expected) profile, and 〈I(μ)〉, the expected intensity distribution for the ensemble, is studied: it is taken as a measure of the relevance ofI(〈μ〉) as an approximation. At very short ranges, the two quantities are identical. At very long ranges, 〈I(μ)〉 obliterates entirely the range dependence ofI(〈μ〉). The usefulness ofI(〈μ〉) as an approximation is therefore restricted to ranges up to some transition rangerT. The transition range is inversely proportional to the relative magnitude ε of the deviation from the mean profile 〈μ〉, and also to ratios constructed from the characteristic (focusing) length of the channel, the injection depth of the beam relative to the channel axis, and the correlation length of the ensemble of profiles. Expressions forrTare derived in several limiting situations, and potential applications are discussed.