Family formation and the life cycle.

Mathematical expressions are developed for certain life cycles when only the age-specific birth and death rates are known. The probability at birth that a woman will have a specified number of children and the expected length of time spent before the first birth, between the first and the last child, and between the last child and the time of the woman's death are shown to be calculable. Expressions for the probability of at least one child outliving the mother and for the expected number of children outliving the mother are also developed and are evaluated for three selected countries with different birth and death rates to show how these life cycles depend on birth and death rates.