Question

3). The life table for Londoners shown in Table 2 was constructed in 1662 by John Graunt who is widely considered to be the inventor of life tables (his London Bills of Mortality culled much information from baptism and death lists in the later plague period) For each question below, give formulaic expressions (e.g. 5qio) first and then estimate (a). The probability that a baby will not survive to 26 years (b). The probability that a person aged 26 will survive to age 46 (c). The average number of years that a baby is likely to survive under this mortality regime (d). How can you interpret the a^s column of a life table? Also (e) for questions (a) to (d) above, state the assumptions that you have made Table 2 life table: Londoners 1662 Exact age Survivors 100 64 40 16 26 36 46 56 16 (Hint: for first years of life, assume the average proportion of the time lived in the age interval is denoted by 0.2). You have.to use your judgment as to how long the last person will survive. The question asks you to state your assumptions. As mentioned in the lectures and in your readings, a, takes on different values at different points in life (e.g. see Newell reading, p. 75). The hints provided should indicate plausible assumptions that you could make for the first years of life Regarding the Tx column (i.e. the total years lived after exact age x), recall that To (i.e. the T. value at age 0) is the summation of the Lx column (in an abridged LT, that's all the values). So, To is the sum of how many years will be lived in the first, second, third, fourth, etc., years of life when all are added together. The T. figure for any other age (e.g. exact age 40) is the sum of the years lived for that age (L) and all later ages by those survivors still alive at the beginning of the age in question. Read carefully what the Table says. The top of column 2 states that this is a column of survivors. As described in your lecture presentations, readings (e.g. Newell, pp. 73-74), and course handouts, the number of survivors at exact age x is the 1, column of a life table. [Do not confuse with px, which refers to the probability of survival]

Answer 1

T フ リ ロイ Nt (L) 0

→Now ni we can see 0-