11. An actuary models the future lifetime of (50) as follows. T (50) has a force of mortality , where has the pdf 9 () = { { g 2 0 < < 100 1002 0 otherwise (a) Find the survival function for T (50). (b) Find the pdf for T (50). (c) Find the mortality rate function for T (70). (d) Approximate the probability that a 70-year-old dies within the next day by using (c). (e) Find the exact probability a 70-year-old dies within the next day by using (c).