ABSTRACT
The study of branching processes has a long history. The subject of branching processes began in 1845 with Ire´ne´e-Jules Bienayme´, a probabilist and statistician, and was advanced in the 1870s with the work of Reverend Henry William Watson, a clergyman and mathematician, and Francis Galton, a biometrician (Mode, 1971). These individuals were interested in studying the survival of family names. Galton in 1873 submitted a problem to the Educational Times (Mode, 1971) stating the following: Suppose adult males (N in number) in a population each have different surnames. Suppose in each generation, a0 percent of the adult males have no male children who survive to adulthood; a1 have one such child; a2 have two, and so on up to a5, who have five. Then Galton posed two questions (Mode, 1971):
(1) Find what proportion of the surnames become extinct after r generations.
