Mortality table. The following American experience mortality table gives the proportion living as a function of age, starting from age 10 in increments of 10 years.
(a) Calculate the percentage dying in each 10-year interval and plot the histogram.
(b) Calculate the average lifespan of 10-year-olds. Use the midpoints of the intervals as the age at death.
(c) Calculate the hazard function for each 10-year interval (as a percent per year) and plot it.
(d) Draw the survivorship curve for 10-year-olds and obtain the 10, 50, and 90% points of the distribution of their lifespans. What proportion of 10-year-olds reach age 65?
(e) Calculate and draw the survivorship curve for 30-year-olds and obtain the 10, 50, and 90% points of the distribution of their lifespans and their expected lifespan.
(f) Repeat
(e) for 50-year-olds. What proportion of 50-year-olds reach age 65? (9) Calculate and plot the hazard function for 50-year-olds and compare it with that for 10-year-olds. What general conclusion does this indicate?