The statistical mechanical ensemble associated with molecular-dynamics (MD) simulations with the weak coupling (WC) thermostat proposed by Berendsen [J. Chem. Phys. 81, 3684 (1984)] is analyzed. Using a generalized Liouville equation, an approximate equilibrium distribution function in the configurational space for the WC thermostat is obtained. From this distribution function, fluctuation formulas associated with the constant volume specific heat C-upsilon, pressure coefficient gamma(upsilon), and isothermal compressibility beta(T) are obtained. The validity of the derived distribution function and the fluctuation formulas were examined in a Lennard-Jones fluid. C-upsilon and gamma(upsilon) calculated from the formulas for the WC thermostat agree very well with those obtained in the canonical or microcanonical MD.