OTHER WORD CHOICES: chance, accidental, haphazard, unsystematic, hit and miss
AND yes, arbitrary is another word for Random.
Here are two off the wall words that I found that also can be synonyms for Random:
Stochastic: (stuh-KAS-tik) adjective: Involving chance; random; probabilistic.
Etymology: From Greek stokhos (aim, target, a pointed stake for an archer to aim at). Earliest documented use: 1662.
Usage: “Medicine is a stochastic science — no doctor can predict the future.” Sandeep Jauhar; When Doctors Slam the Door; The New York Times; Mar 16, 2003.
Ergodic: (ərˈgädik) of or pertaining to the condition that, in an interval of sufficient duration, a system will return to states that are closely similar to previous ones: the assumption of such a condition underlies statistical methods used in modern dynamics and atomic theory.
An easier way of saying this is: a system will randomly change states but will eventually return to its original state.
Etymology: early 20th century (1926) from German ergoden, from Greek ergon ‘work’ + hodos ‘way’ + -ic
Usage: In an ergodic forest, while the size, shape and spacing of individual trees may vary, their distribution in any given area is the same as any other area. http://www.thefreelibrary.com/Theoretical+speed+above+which+birds+and+drones+are+sure+to+crash…-a0277579590