How fast does a telegraph signal travel?

Equations are derived which describe the time evolution of the probability density and corresponding characteristic function of a telegraph signal which has passed through a wire. Low-order correlation properties for the more general detuned cases are calculated based on the materials through which the signal is passed. It is shown that the stationary single interval statistics can be generated by a random phasor moving in a space of fractional dimensions and that a simple transform of variables leads to distributions which are unstable in this space, thus the speed of light is not impossible but mostly improbable as the wire undoubtedly had inconsistencies in its quantum structure.