He earned bachelor (magna cum laude) and Master of Science degrees in electrical engineering from the University of North Dakota through the Air Force Institute of Technology program in 1964 and 1965, respectively.

He completed Squadron Officer School in 1959, and Air Command and Staff College as a distinguished graduate in 1969, concurrently earning a master's degree in business administration from Auburn University.

Randolph then attended graduate school at the University of North Dakota until July 1965 and then was assigned to Los Angeles Air Force Station, California, as Chief, On-orbit Operations, Space Systems Division.

From August 1968 to October 1969, Randolph concurrently attended Air Command and Staff College at Maxwell AFB and pursued another master's degree via Auburn University's Montgomery, Alabama campus.

In this capacity he managed a program to design and develop the U.S. anti-satellite system with its supporting surveillance, command and control, and survivability aspects.

He returned to Air Force headquarters in May 1985 and served as deputy chief of staff for research, development and acquisition.