Mr Baxter was born in Bearstead Jewish Maternity Hospital, Stoke Newington; his family lived in Ilford, Essex. He was educated at Ilford County High School (where he was a prefect) and University College London; his father had also been to UCL.
His first job (1975-7) was at an insurance company. He then went to the Central Electricity Generating Board, where he researched ways to predict the available generator capacity given the incidence of breakdowns and the time to repair generators. This work was accepted by UCL for a PhD in 1980.
Dr Baxter was then offered a temporary post as a lecturer at the University of Delaware. The next year, he moved to the State University of New York at Stony Brook (SUNY); he was given a tenured position there about ten years before his death from cancer.
As a mark of the high regard in which he was held by his colleagues, SUNY established the annual Laurence Baxter Memorial Lecture, which is now given each April at Stony Brook. Many distinguished statisticians, such as Herbert Robbins and Bradley Efron, have delivered the lecture.
Dr Baxter was intensely interested in films. He had the unusual distinction for a non-professional of being a Fellow of the British Film Institute, and briefly acted as film reviewer for a Delaware radio station.