1. Suppose that qx is equal to a constant q for all x. Find expressions in terms of q and n for (a) npx, (b) ex. Do you think that this gives a realistic life table? Why or why not?
2. In constructing a life table for heavy smokers, Actuary A decides to take a standard table, and double each value of qx, using a value of 1 if qx > 0.5. Actuary B takes the same table and squares each value of px. Show that the resulting table of Actuary B, has lower mortality rates at all ages than that of Actuary A.