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On the parity of individuals in birth and death processes

This paper deals with the parity of individuals in an age-dependent birth and death process. A more general model with parity and age-dependent birth rates is also considered. The mean number of individuals with parity 0, 1, 2, ·· ·is obtained for the two models. The first moments of the total number of births in the population up to time t and the sum of the parities of the individuals existing at time t are obtained. A brief discussion on the parity of individuals in a population including ‘twins' is also given.