For this question, how do you know tPx*(Mu)x+t= constant = qx (0<=t<=1) for decrement a?? And for decrement c, why is tPx=1 (0<t<1/4) and tPx= Px (1/4<=t<1) provided that decrement c takes place at time 1/4 only. Thanks very much if someone can help?
For the first part - it's just that decrement a occurs uniformly in the single decrement table and what you've typed out is the definition of uniform distribution of decrements - it's just like UDD assumption in chapter 3 of the course, except now there's a general unspecified decrement and not death (but the assumption's the same). For decrement c - it only operates at time 0.25. So up to then, you're certain to survive decrement c (as it's not operating and can't "get you"). So it's certain that you'll survive decrement c up to time 0.25 giving the probability of survival of 1. It's the same idea for the other part of it. Decrement c only operates at 0.25 so if you survive c past then, you'll definitely survive c for the whole year.
