Statistics Analysis

1. (a) Suppose we have two independent lives aged 40 and 50 respectively. Using the actuarial tables provided, calculate the following assuming that Aiwa = 0.13, ./16,r0 = 0.35 and i =5% p.a. Clearly state any approximations you make. (i) 204740:50 (i) A(4102:50) :20
   6 marks Consider two independent lives initially aged x and y respectively. Explain the meaning of and nqs.y2 , and prove that
   nqtY nqx2 // = nq•
   4 marks Suppose that /ix denotes the force of mortality for a life aged x, and a denotes the force of interest.
   (i) Show that:
   a = i e-stfpx ::.. ax 0 + 2 dt AZ). CO 1 1 0 Hint: Use the Woolhouse formula (stated below) with g(t) = e-sttp. and h =1.
   c° h2 L g(t)dt = liEg(kh)— .ig(0)+ g'(0) — • • • tc)
   (ii) Use the Woolhouse formula to show that: —4 8 1 8405 . _

Sample Solution

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