1. Duration of life as a random variable -- 2. Models of distribution functions F(x) and force of mortality u(x) -- 3. The empirical distribution function of duration of life -- 4. Deviation of F?n(x) from F(x) as a random process -- 5. Limit of empirical process : Brownian bridge ; Distribution of x2 goodness of fit statistic -- 6. Statistical consequences of what we have learned so far ; two-sample problems -- 7. Testing parametric hypotheses. Unexpected example - exponentiality of durations of rule of Roman emperors -- 8. Estimation of the rate of mortality -- 9. Censored observations ; Related point processes -- 10. Kaplan-Meier estimator (product-limit estimator) for F -- 11. Statistical inference about F, based on the Kaplan-Meier estimator -- 12. Life insurance and net premiums -- 13. More on net premiums. Endowments and annuities -- 14. Annuities certain ; Some problems of general theory -- 15. Right-tail behavior of F?n ; Non-parametric confidence bounds for expected remaining life -- 16. Population dynamics.