1. In a double-decrement model with decrements of (d) for death and (w) for withdrawal, we are given that deaths are uniformly distributed over each year of age in the single-decrement table, while one-third of the withdrawals in any year take place in the middle of the year and two-thirds occur at the end of the year. Given that q′(1) = 0.20, q′(2) = 0.36. Calculate q(1) and q(2).
2. In a multiple-decrement model with three decrements, failures from causes 1 and 2 both occur uniformly over each year in the single-decrement table. For cause 3, 60% of the failures in any year occur 1/4 of the way through the year and the other 40% occur 3/4 of the way through the year. Find formulas that give the unprimed rates in terms of the primed.