Using a Monte Carlo method, we simulate the measurement, by the 2E technique, of the average prompt neutron multiplicity as a function of the mass of fragments from the thermal neutron induced fission of 239Pu. The input data for the simulation, associated with the primary fragment mass (A), consist of the yield (Y ), the distribution of the total kinetic energy characterized by its average (¯TKE) and its standard deviation (σTKE), the average prompt neutron multiplicity (¯νs, a sawtooth approach of experimental data), and the slope of neutron multi-plicity against total kinetic energy (dνs/d < TKE >). The output data, associated with the simulated as the fragment mass measured by the 2E technique (µ), consist of the yield (y), the distribution of the total kinetic energy characterized by its average (tke) and its standard deviation (σtke), and the average prompt neutron multiplicity (¯νµ). In the mass regions A ≈ 115 and A > 150, ν¯µ is higher than ν¯s. This result suggests that, in those mass regions, the 2E experimental values associated with the average neutron multiplicity are overestimated, referred to the corresponding to the primary fragments