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An electromagnetic pulse propagating through the ionosphere can be modified owing to dispersion as well as random scattering from electron density irregularities. As a result, the pulse arrival time and the pulsewidth are altered. In this paper we show how such quantities can be computed and related to the medium parameters. In this connection the two-frequency mutual intensity function enters in the formulation naturally. The results show that the mean arrival time is dominated by a term which indicates that the pulse is traveling at the group velocity corresponding to the carrier frequency. But there are also small but important corrections resulting from random scattering and higher order dispersion. Our results also show the importance of scattering and dispersion in lengthening the pulse. These results have important implications in satellite based navigational and communication systems.