In the attached photo I am not able to understand how n|qx and p[Kx=k] has those expressions.please help asap. P.s I haven't done ct4
n|qx is the deferred probability that a person now aged x lives for another n years, so npx and then dies within age x+n and x+n+1, so qx+n. qx+n can also be written as 1qx+n, that is he who is aged x+n dies between the period n and n+1. P(Kx=k) is the probability that a person now aged x will survive for the next k years and die within the next moment or instant. So P(Kx=k) is equal to kpx*qx+k, that is the probability that a person now aged x lives for another k years (kpx) and then dies within the next moment (1qx+k or simply qx+k). Hope this helps. Regards. Shyam
Actually P(Kx=k) means the probability that the person dies anywhere in the year between time k and time k+1, not at the "moment". Notice that qx+k is also the probability of dying between x+k and x+k+1. I think Shyam may be thinking of the PDF of Tx, which would be kpx*mu(x+k). (mu relates to the moment of death, q relates to death over a whole year of age.) Best wishes Robert