{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

PQ-5-331-2011-F

# PQ-5-331-2011-F - Practice Questions 5 ACTSC 331 FALL 2011...

This preview shows pages 1–2. Sign up to view the full content.

Practice Questions 5 – ACTSC 331, FALL 2011 1. For two independent lives (40) and (50), you are given: For (40), mortality follows μ 40+ t = 0 . 01 , t 0 . For (50), mortality follows μ 50+ t = 0 . 015 , t 0 . Calculate the probability that (50) will die between ages 70 and 80 after (40) dies. 2. You are given that T x and T y are independent. The following life table: k q x + k q y + k 0 0.08 0.10 1 0.09 0.15 2 0.10 0.20 Calculate the probability the first death occurs after 2 years before 3 years from now. 3. Assume that T 30 and T 40 are independent. You are given: (i) For (30), mortality follows l x = 100 - x, 0 x < 100. (ii) For (40), mortality follows μ 40+ t = 0 . 01 , t 0 . Calculate (a) Pr { T 30:40 > 20 | T 30 50 } ; (b) the probability that (30) will die after (40); (c) V ar [ T 30:40 ]; and (d) E [ K 30:40 ] . 4. For two independent lives (50) and (60), you are given: For (50), mortality follows μ 50+ t = 0 . 02 , t 0 . For (60), mortality follows l x = 90 - x, 0 x < 90 . Assume that (50) and (60) are subject to a common shock. The time of the shock is assumed to be an exponential random variable with mean 25. (a) Calculate the expected time of the first death of (50) and (60). (b) Calculate the probability that (50) and (60) will die at the same time. (c) Calculate the probability that the second death occurs in year 7. 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
(d) A fully continuous insurance is issued to (50) and (60). A death benefit of 1,000 is payable at the moment of the first death. You are given δ = 0 . 04. Calculate the expectation of the present value of the death benefit.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

PQ-5-331-2011-F - Practice Questions 5 ACTSC 331 FALL 2011...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online