Hi In assignment X5, question 5(ii) In solution, the alternative answer where there is only 1 integral, I can understand 1P(50+t-1)(iibar) is the prob of staying in sick state for 1 year, but v(50+t) is the prob of the life dies at 50+t? But in the question it says "life has been sick for at least a year", it seems the alternative answer only count for life that dies exactly after sick for 1 year, but did not count life is sick for more than 1 year? Did I miss something? Thanks a lot!!
Hi, So taking each probability term in the integral in turn: t-1p50(ai) - the probability that the life was in the able state at age 50 but the sick state at age 50 + t - 1 (ie one year ago) 1p50+t-1(iibar) - the probability that the life has remained sick over the last year nu(50+t) - the probability the life transitions to the dead state from the sick state at age 50 + t So this works: prob life was ill a year ago, has remained ill for the last year, then transitions to dead state at time t. Hope this helps. Joe
