A simple Jeffcott rotor with both external and internal damping is considered. The rotor is subject to a random excitation which results in transverse random vibrations even at rotation speeds below the instability threshold. The random forces in two perpendicular directions are assumed to be uncorrelated white noises which may have different intensities in general. An analytical expression is derived for peak value of coherence function of responses in these directions as a function of ratio of rotation speed to its value at the instability threshold. Numerical simulation results are presented for verification of the corresponding coherence-based method for on-line stability margin evaluation for rotating shafts.