We know that d(tqx)/dt = tPx * mu_(x+t) However, according to ch.6, Page 6, mu_(x+t) = (lim h->0+) P[T<=x+t+h | T > x+t] / h I put t = 0, mu_x = (lim h->0+) P[ T<=x+h | T > x] / h since P[T<=x+h | T > x] is hqx, so mu_x = (lim h->0+) hqx/h Since 0qx = 0, then mu_x = (lim h->0+) (hqx - 0qx)/h Now the RHS is same as d tqx/dt, so d tqx/dt = mu_x ? I am very confused. Please help on the above. Thanks a lot!!
Hello You've shown that d(tqx) / dt evaluated at t = 0 is equal to mu_x, which is correct as it is 0px * mu_x and 0px is 1. In your final line, the RHS is the derivative of tqx evaluated at 0. Hope this helps! Andy
