3. You are given (i) Z = 1,000vK30+1, 2,000v K30+1, K30 = 0, 1, 2,...,9 K30 > 10 (ii) Z = - 50TV, Tz < 20 TT > 20 1,000, (a) Describe in words the insurance benefits with the present values given above. (b) Find expressions (in terms of the standard actuarial notations) for the expected value of Z and Z2, respectively. (c) If i = 0.05 and the mortality follows the LTAM Standard and Ultimate Life Table, calculate the expectation of Z. (d) If 8 = 0.06 and the force of mortality 0.03 for all a > 0, calculate the expectation of Z2.