# AS 5102 Study Guide - Midterm Guide: Life Table, Cumulative Distribution Function

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Published on 23 Nov 2019

School

Department

Course

Professor

TEMPLE UNIVERSITY

AS 3501/5102 ACTUARIAL MODELING I, SPRING 2018

EXAM 1, 2:00-2:50 PM, FEB 19, 2018

•For undergraduate students, there are 4 problems and 35 points in total. For graduate students, there

are 5 problems and 40 points in total.

•You must show your work in the blue book. No credit will be given for unsupported answers.

•Clearly mark all ﬁnal answers.

1. (8 points) In this question, simplify where possible.

(a) Express the following probabilistic statements in Actuarial notations (such as tqx,tpx, etc).

(i) The probability that a life aged 20 dies between age 30 and age 50.

(ii) The probability that a life aged 50 dies within 20 years, given that the life survives to age 60.

(b) Simplify the following expressions into a single (actuarial) notation and explain the probabilistic

meaning (similar to the probabilistic statements in part (a)):

(i) S30(25)

S30(10)

(ii) 10p20−10|5q20

5p20

2. (10 points) You are given the following select life table:

x l[x]l[x]+1 lx+2 x+ 2

60 96568.13 96287.48 95940.60 62

61 96232.34 95920.27 95534.43 63

62 95858.91 95511.80 95082.53 64

63 95443.51 95057.36 94579.73 65

64 94981.34 94551.72 94020.33 66

Calculate

(a) d63

(b) 1|2q[60]

(c) 2-year temporary curtate life expectancy of a life aged 61 and selected at age 61 (i.e., e[61]:2).

(d) Under the Constant Force of Mortality fractional age assumption, calculate 0.3|0.4q[60]+0.5

(e) Under the UDD fractional age assumption, calculate ˚e[63]:2

3. (8 points)

(a) Explain, in one sentence, the meaning of µx·∆xfor a small quantity of ∆x, where µxdenotes

the force of mortality of a life at age x.

(b) Given that

F0(x) = 1 −35

c+x3

, for x≥0.

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