Answer all the questions that provided

Exercise 2.1 Let Fo(t) = 1 - (1 - t/105) / for 0

t/105)l/5 for O s t s 105. Calculate Exercise 2.1 Let Fo(t) 1 (a) (b) (c) (d) (e) (f) (g) the probability that a newborn life dies before age 60, the probability that a life aged 30 survives to at least age 70, the probability that a life aged 20 dies between ages 90 and 100, the force of mortality at age 50, the median future lifetime at age 50, the complete expectation of life at age 50, the curtate expectation Of life at age 50. Exercise 2.2 The function 18000 110x-x2 18000 has been proposed as the survival function SO(x) for a mortality model. (a) What is the implied limiting age w? (b) Verify that the function G satisfies the criteria for a survival function. (c) Calculate 20m. (d) Determine the survival function for a life aged 20. (e) Calculate the probability that a life aged 20 will die between ages 30 and 40. (f) Calculate the force of mortality at age 50. Exercise 2.3 Calculate the probability that a life aged O will die between ages 19 and 36, given the survival function o s x s 100 w). 10 Exercise 2.4 Let SO (x) = exp Ax + Bx2 + DX where A, B, C and D zue all positive. log D log D