Consider a population in which three decrements are acting, mmQ-

\y{a\{b\{c).

(i) Write an expression for the probability that a 40-year-old will leave the population because of decrement {b) at age 47 last birthday,

(ii) Write an expression for the probability that a 40-year-old will leave the population because of decrement

(b) or (c)

between ages 44 and 48.

(iii) Write formulae for q^^ and W3Q

.

(iv) If it is discovered that q^^^ + ^1^^ = 1 - p^P for all x > 50, what can you conclude about decrement (c)?