CHAPTER II

PROBABILITIES OF DEATH AND SURVIVAL

1. Starting with the values of qx, we have in the first chapter deduced the columns lx and dx of the Life Table. We are now in a position to find the values of more complicated probabilities.

The symbol (x) is to be read as "a life now aged exactly x." We have defined npx=l%" as the probability that (x) would

live at least n years longer, or that such a life would die at an age higher than x+n.

Also, I nQx = Q1 TI =1—,,px = lx llx+n has been defined as the

x

probability that (x) will die during the next n years or the probability that (x) will fail before the period of n years has elapsed, or the probability that (x) will not live n years.

2. Consider two lives (x) and (y) and assume that the death or survival of the one will not affect the death or survival of the other. The product („px+ I nQx) (npy+ „Qy), which is 1 X1, can be ex-

panded as, npx • npy+"px • I nQy+npy' (nQx+ I nQx • I nQy•

We proceed to examine the meaning of each of these four terms:

(1) Both (x) and (y) may survive n years, the probability being npx • npy which is written npx, and which =1— InQxy =the complement of the probability that the pair will be broken during the next n years.

Or 1—Qx'y„ =the complement of the probability that the pair will be broken first, before the n years are ended.

Or Qxy =the probability that the n years will elapse before the pair is broken.