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Closed-form expressions for the turbulent mean reaction rate and its covariance with the temperature are derived for premixed and non-premixed combustion. The limit of large activation energies is exploited for a chemical reaction rate that, by virtue of coupling functions, depends on the mixture fraction and a non-equilibrium progress variable only. The probability density function (p.d.f.) formulation with an assumed shape of the p.d.f. is used; a beta-function distribution is assumed for the progress variable. The mean reaction rate is expressed in terms of the mean and the variance of the temperature and, for non-premixed combustion, of the mixture fraction. The reaction kinetics are represented by the non-dimensional activation energy and the laminar flame velocity. For non-premixed systems the possibility of local extinction by flame stretch is considered.