Let nlm^x denote the probability that a person aged x will die between ages x -\- n and x -'r n + m. (When w = 1 it is omitted in this notation.)

(a) Show that ,U^, = ^-^n-Un^m

(b) Show that „|;„^;f = np^ — n+mPx- Explain this identity verbally.

(c) Show that n\mqx = nPx(^ - mPx+n)- Explain this identity verbally.

7-1 1. You are given the following probabilities:
(i) That two persons age 35 and 45 will both live for 10 years equals .80.
(ii) That a person age 60 will die within 5 years, whereas another person age 55 will live for 5 years is .05.
(iii) That a person age 35 will live 30 years is .60.
Find the probability that a person age 35 will die between ages 55 and 60.