I just have a quick question here about survival probability tPx. Its the definition that tPx = exp(∫Ux+s ds), integrating from 0 to t. But for Q 1.19 from Q&A Bank part 1, when calculating the probability of a 60 year old surviving to age 80, it integrates from 60 to 80 rather than 0 to 20. Can anyone tell me why?? Many thanks.
If you look closely you'll find that the equation now reads (or should do): tPx = exp(∫Us ds), integrating from 60 to 80. The term inside the integral is Us rather than Ux+s, so if you rewrite it from the way the core reading suggests, you'd have tP_60 = exp(∫U_60+s ds), integrating from 0 to 20. I hope this makes sense?
