Math 472 Spring 2011 Chapter 9 Lecture Examples

# Math 472 Spring 2011 Chapter 9 Lecture Examples - MATH...

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MATH 472/567: Actuarial Theory II/Topics in Actuarial Theory I Chapter 9: Lecture Examples 1. You are given: (i) (x) and (x + 3) are independent lives. (ii) 6 q x = 0.20 Calculate the probability that (x) and (x + 3) both survive the next 3 years. 1

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2. You are given: (i) (25) and (35) are independent lives. (ii) Each life has mortality that follows de Moivre’s Law with limiting age 100. (iii) Both (25) and (35) were born on January 1. Calculate the probability that both (25) and (35) will die in the same calendar year. 2
3. Consider two independent lives: a 30 year old male and a 28 year old female. (i) The age-at-death for males follows a uniform distribution on [0, 100]. (ii) The age-at-death for females follows a uniform distribution on [0, 110]. (a) Calculate the probability that both (30) and (28) survive the next 20 years. (b) Determine the expected time until the ﬁrst death of (30) and (28). (c) Find μ 30:28 (20). (d) Determine an expression for the pdf of T (30 : 28). 3

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4. For a population of smokers and non-smokers: (i) Non-smokers have a force of mortality that is equal to one-half of the force of mortality for smokers at each age. (ii) For non-smokers:
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Math 472 Spring 2011 Chapter 9 Lecture Examples - MATH...

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