Moran was educated at Sydney U and Cambridge U and was a researcher at Oxford U from 1946 to 1951, before returning to Australia. He was the founding Professor of Statistics at ANU, where his research students included Hannan and Heyde. He was elected to the AAS in 1962, and was elected FRS in 1975. He was the first President of the Australian Statistical Society (now the SSAI) in 1963 and was awarded the Society's Pitman Medal (see Pitman) in 1982. He was President of the Australian Mathematical Society in 1976.

http://science.org.au/fellows/memoirs/moran.html Fuller biography and photograph.