'randomly-distributed' originates from the combination of 'randomly' and 'distributed'. 'Randomly' comes from 'random', which originates from Old French 'randir', meaning 'to gallop', and 'distributed' comes from Latin 'distribuere', where 'dis-' meant 'apart' and 'tribuere' meant 'to assign'.

'Randomly-distributed' evolved from the combination of 'randomly' and 'distributed', which were used separately in Middle English and later combined in modern English to describe a lack of pattern in distribution.

Initially, 'randomly' meant 'without a specific pattern', and 'distributed' meant 'spread out'. Together, they describe a distribution without a specific pattern.