Problems arising when averaging fast signals random in shape and occurrence time are systematically examined. A setup is described, comprising a sampling oscilloscope and a memory unit, allowing high speed random operation. The system logic, which insures one‐to‐one delay‐channel correspondence under the most stringent conditions, allows averaging signals satisfying various specified conditions and optimizes the statistical accuracy of the results. An add‐subtract method allows elimination of synchronous transient noise, either external or arising from the sampling unit itself. Signals of 30 &mgr;V were averaged out in this way with a 0.1 nsec instrumental risetime. Applications are shown to a broad range of problems which include fast signal enhancement, optical signal measurements, photomultiplier single electron response studies, illumination function measurements for fast organic and slow scintillators, and semiconductor detector risetime observation. Two‐dimensional representation of random signal properties is also shown. It allows, for example, time jitter determinations with some tens of picosecond precision. The setup allows direct measurement of noise correlation and cross correlation functions.