Actl 1001 Past Paper

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ACTL 1001 Actuarial Studies and Commerce Class Test 1 Monday, 25th August 2008 Time Allowed: 55 minutes Total Mark: 100 points Total Assessment credit: 11% Write your name and student number on the space provided:

Name:______________________________

Student ID:__________________________

Read through the following information carefully. You can only go to the next pages when told to do so. This class test consists of 6 problems requiring short-written answers. Marks allocated for each problem are as indicated. You may use your own calculator for this exam. You can only start writing down your solutions and answers when told to do so Answer the problems you are most con…dent with …rst. Anyone writing after time has expired will be given a mark of zero. A list of equations can be found in the last page of this booklet. GOOD LUCK!

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1. [20 marks] q If s (x) = 1

x 80

for 0

x < 80 calculate the probability that

(a) [5 marks] a life aged 15 will survive to age 45 (b) [5 marks] a newborn will die before age 40 (c) [5 marks] a life aged 20 will die between age 45 and 65 (d) [5 marks] q40

2

.

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2. [13 marks] A random variable X can take the values 1; 2; ::; 4, each with equal probability. Determine (a) [4 marks] the Expected Value of X (b) [5 marks] the Standard deviation of X: (c) [4 marks] E [X 3 ] :

4

.

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3. [26 marks] You are given the following life table Age 70 71 72 73 74 75 76 77 Find: (a) [5 marks] The value of l72 (b) [5 marks] The probability that a 74 year old will not survive to age 76 (c) [7 marks]

4j1 q70

dx lx Tx 374 3385 365 349 330 2297 1967 1659 1376 1122 9838

(d) [9 marks] e75

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.

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4. [7 marks] Insurance company premium rates for term insurance (for a given age and sex) di¤er depending on whether the life insured is a smoker or a nonsmoker. Non-smokers have lower premium rates as they have lower death rates. Suppose an insurance company wishes to remove discrimination due to...