CHAPTER XI
EXAMPLES

1. Given that q, = x   -45 for values of x from 90 to 100 inclusive, 100

and that /90 =1,000, form the l and d columns starting at age 90. What stationary population can be supported by 1,000 annual entrants aged 90?

2. If dx = k +cx and /Ho =duo= 1, find ho and iopio in terms of either k or c.

3. If lx =ksxwx2g`x for all values of the variable x obtain an expression for the force of mortality.

4. Assuming a uniform distribution of deaths prove that

(zpx —ps) +(2px -2px) +(zpx -3Px) +etc. =

5. There are three lives (x), (y) and (z). You are given that qx = .02, qy = .025, and qZ = .03. Find the probabilities of all the different possibilities that may happen as regards death and survival during the next year. Find the sum of these probabilities.

6. Given lop3o =.920, lop4o = .890 and p4o =.991, calculate the probability that a person aged 30 will die (i) before age 50, (ii) between ages 40 and 50, (iii) in his 41st year.

7. The probability that a man aged 20 and another man aged 40 will both be alive at the end of 20 years is .4. Out of 96,000 men alive at age 20, 6,000 will die before they attain age 30. Find the probability that a man now aged 30 will die within the next 30 years.

8. Three men, A, B and C, are all of the same age x. Express the following probabilities: (i) That A alone will be living at age x+n.