fall2010Homework - STAT 490 Actuarial Models Homework -...

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STAT 490 Actuarial Models Homework - Fall 2010 November 12, 2010 Chapter 3 1. You are given that 0.02 . Calculate: a. () Fx b. sx c. fx d. EX e. Var X f. 0 x q g. 0 x p h. 40 0 q i. 40 0 p j. Pr(40 60) X  k. x l. (75) m. tx q n. p o. 75 t q p. 75 t p q. [ ( )] E T x r. [ (75)] ET s. x e t. 0 e u. 75 e v. [ (75)] Var T w. mx x. (75) m y. x T z. 75 T aa. 75:10 e bb. 10 75 L cc. nx m dd. 40 m ee. 10 75 m ff. | n m x q gg. 10|5 75 q
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STAT 490 Actuarial Models Homework - Fall 2010 November 12, 2010 2. Mortality follows DeMoivre’s law with 125 . Calculate: a. () Fx b. sx c. fx d. EX e. Var X f. 0 x q g. 0 x p h. 40 0 q i. 40 0 p j. Pr(40 60) X  k. x l. (75) m. tx q n. p o. 75 t q p. 75 t p q. [ ( )] E T x r. [ (75)] ET s. x e t. 0 e u. 75 e v. [ (75)] Var T w. mx x. (75) m y. x T z. 75 T aa. 75:10 e bb. 10 75 L cc. x e dd. 0 e ee. 75 e ff. nx m gg. 40 m hh. 10 75 m ii. | n m x q jj. 10|5 75 q
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STAT 490 Actuarial Models Homework - Fall 2010 November 12, 2010 3. You are given 2 0 10,000 t t q for 0 < t < 100. Calculate: a. () Fx b. sx c. fx d. EX e. Var X f. 0 x q g. 0 x p h. 40 0 q i. 40 0 p j. Pr(40 60) X  k. x l. (75) m. tx q n. p o. 75 t q p. 75 t p q. [ ( )] E T x r. [ (75)] ET s. x e t. 0 e u. 75 e v. [ (75)] Var T w. mx x. (75) m y. x T z. 75 T aa. 75:10 e bb. 10 75 L cc. nx m dd. 40 m ee. 10 75 m ff. | n m x q gg. 10|5 75 q 4. (Spreadsheet) You are given that mortality follows the Illustrative Life Table. Use the spreadsheet on the class website to calculate: a. 40 0 q b. 40 0 p c. Pr(60 80) X d. 10 75 p e. 10 75 q f. (75) m g. e h. 75 e i. 10|5 75 q 5. You are given that 2 100 x x for 0 100 x  . Calculate and 10 50 p .
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STAT 490 Actuarial Models Homework - Fall 2010 November 12, 2010 6. You are given that mortality follows Gompertz with 0.01 B and 1.1 c . Calculate a. (10) b. 10 20 p c. 10 20 q 7. You are given that mortality follows Weibull with 0.00375 k and 1.5 n . Calculate a. b. 10 20 p c. 10 20 q 8. (Spreadsheet) Download STAT 490 Problem 8.xlsx from the class website and complete Columns C through H. 9. Assume that mortality follows the Illustrative Life Table for integral ages. Assume that deaths are linearly distributed (UDD) between integral ages. Calculate: a. 0.5 80 q b. 0.5 80 p c. (80.5) d. 1.5 80 p e. 1.5 80 q f. 0.5 80.5 q g. 0.5 80.25 q 10. Assume that mortality follows the Illustrative Life Table for integral ages. Assume that probability of survival is linearly distributed (Constant Force) between integral ages. Calculate: a. 0.5 80 q b. 0.5 80 p c. (80.5) d. 1.5 80 p e. 1.5 80 q f. 0.5 80.5 q g. 0.5 80.25 q 11. Assume that mortality follows the Illustrative Life Table for integral ages. Assume that probability of survival follows a hyperbolic curve (Balducci) between integral ages. Calculate: a. 0.5 80 q b. 0.5 80 p c. (80.5) d. 1.5 80 p e. 1.5 80 q f. 0.5 80.5 q g. 0.5 80.25 q
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STAT 490 Actuarial Models Homework - Fall 2010 November 12, 2010 12. You are given the following select and ultimate mortality table of x q ’s. [] x x q [ ] 1 x q [ ] 2 x q 3 x q 3 x 50 0.020 0.031 0.043 0.056 53 51 0.025 0.037 0.050 0.065 54 52 0.030 0.043 0.057 0.072 55 53 0.035 0.049 0.065 0.091 56 54 0.040 0.055 0.076 0.113 57 55 0.045 0.061 0.090 0.140 58 Calculate: a. [54] p b. [53] 1 p c. [52] 2 p d. [51] 3 p e. 54 p f. 5 [54] p g. 2|2 [52] q h. A life policy insurance policy was issued two years ago to (52). Calculate the probability that this person will live to age 59.
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This note was uploaded on 02/17/2012 for the course STAT 490 taught by Professor Na during the Fall '11 term at Purdue University-West Lafayette.

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fall2010Homework - STAT 490 Actuarial Models Homework -...

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