AN INTRODUCTION TO THE THEORY OF
LIFE CONTINGENCIES

CHAPTER I
THE LIFE TABLE

1. Suppose that we could trace a great many human lives of the same type from birthday to birthday, noting the number who attained each exact age and the part of that number who died before attaining the next age. For example, suppose that we had 100,000 lives aged exactly 50 and that of this 100,000 there were 1.600 who died before attaining age 51: we would be justified in deducing probabilities of death or survival of another life of the same type during the same life year. Of such another life we could say that the probability of surviving from age 50 to age 51 was .984 and the probability of dying within the year was .016.

Such probabilities of death and survival from age to age have been calculated for many types of lives—male and female, insured lives, pensioners, Englishmen, Americans, etc.

2. Defining qx as the probability that a life aged exactly x will die before attaining age x+l, i.e., will not die after age x+l, and px as the probability that a life aged exactly x will attain age x+l, i.e., will not die before age x+1, we have px+qx =1 for any value of x.

3. Suppose that the values of px and qx for every age have been ascertained for a particular class of lives. We can make what is called a Life Table. Defining lx as the number who attain exact age x out of 10 born alive and dx as the number who out of the same to die between the ages of x and x+1, and knowing the values of px and qx for all values of x, we start with the arbitrary radix (an assumed number for lo).