ETC1010_2011_S2 Exam Questions All Topics

7/25/2019 ETC1010_2011_S2 Exam Questions All Topics

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ETC1010 Data modelling and computing

PAST EXAMS

2011 Semester Two

Questions - All Topics


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Question 1 (20 MARKS)

Jester Pty Ltd is a discount airline company that provides no frills air travel between Melbourne andSydney. Passengers receive no free refreshments, no in-flight entertainment, and no seat cushions.Jester operates the Boring 070-200. These aircraft have seating for 200 paying passengers.

Jester flies 365 days per year on several routes using 10,000 flying hours per year total. Each planeneeds a major servicing after 365 days, OR500 flying hours, whichever comes first.

These major servicings take 20 days and cost $150,000. Each aircraft is unavailable for 10 days peryear for other reasons including painting and pilot training. Jester considers that each plane shouldaverage not more than 3 hours scheduled flying per day. Jester is concerned about their scheduledmaintenance costs.

Table 1 shows a spreadsheet model constructed to help with this problem. Table 2 shows data tablesrelating planes, flying hours per day, number of servicings per year, and total servicing cost. Figure1 shows the corresponding chart.

Working Days 365

Total hr/year 10000

Calendar Servicing Interval 365

Hour Servicing Interval 500

Servicing Duration 20

Servicing Cost $150,000

Other unavailable days 10

Planes 10

Annual hr/plane 1000.0Annual servicing/plane 2.0

Days unavailable/plane 50.0

Days available/plane 315.0

hrs/day/avail plane 3.2

Total Annual Servicing Cost $3,000,000.0

Table 1. Spreadsheet Model

Figure 1. Planes and Daily Usage

0

0.5

1

1.5

2

2.5

33.5

4

4.5

0 10 20 30 40

hr/day

perplane

Planes


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Planes Hr/day Planes

Annual

Servicings/plane Planes

Total Annual

Service Cost

3.2 2.0 $3,000,000.0

8 4.098361 8 2.5 8 3000000

9 3.577818 9 2.222222 9 3000000

10 3.174603 10 2 10 3000000

11 2.853067 11 1.818182 11 300000012 2.590674 12 1.666667 12 3000000

13 2.372479 13 1.538462 13 3000000

14 2.188184 14 1.428571 14 3000000

15 2.030457 15 1.333333 15 3000000

16 1.893939 16 1.25 16 3000000

17 1.774623 17 1.176471 17 3000000

18 1.669449 18 1.111111 18 3000000

19 1.576044 19 1.052632 19 3000000

20 1.492537 20 1 20 3000000

21 1.421464 21 1 21 315000022 1.356852 22 1 22 3300000

23 1.297859 23 1 23 3450000

24 1.243781 24 1 24 3600000

Table 2. Data Tables - Average Profit, and number of Meals Carried

(a) Construct a model concept diagram relating the variables used for this problem.(6 marks)

(b) Show a mathematical model for Annual Servicing/plane value (2.0) in Table 1.(4 marks)

(c) Refer to table 2. Note that the Annual Servicing/plane values decrease as the number ofplanes increases. However, this value becomes a constant for 20 or more planes. Explain whythis is this reasonable.

(3 marks)

(d) Using this problem, explain the difference between an intermediate variable, and an inputvariable. Comment on a suggestion that there will never be more intermediate variables thaninput variables.

(3 marks)

(e) What decision(s) should Jester take? Interpret the output variable value that would beobtained. Based on your recommendation, is Jester better off to decide on one more, or onexfewer?

(4 marks)


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Question 2 (40 MARKS)

You have been asked by Original Energy, an electricity retailer, to do some research. They wouldlike to know whether the installation of smart meters, which measure electricity consumptionevery hour, results in consumers using less electricity overall. They have provided data from asurvey of their customers, and expect you to undertake the analysis using Excel.

The following variables are used:

Dependent variable:

USAGE = Amount of electricity used per month by the household (in kilowatthours)

Explanatory variables:

INCOME: = Yearly household income (in $10,000s)

TV: = Number of TVs owned by the household

SMART METER = Dummy variable: 1 = Smart meter installed; 0 = otherwise

HHSIZE: = Number of individuals living in the household

HHSIZE2: = Number of individuals squared

INNER: = Dummy variable: 1 = household in inner city; 0 = otherwise

SUBURBS: = Dummy variable: 1 = household in suburbs; 0 = otherwise

RURAL: = Dummy variable: 1 = household in rural area; 0 = otherwise

All households are categorised as being located in the inner city, the suburbs or a rural area.

An (incomplete) regression output follows on the next page.


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(f)

What would we use the F-statistic and corresponding p-value to test for, in the aboveregression? Sketch (roughly) the F distribution, and indicate the relative locations of the F-stat (from the regression), F-crit (which is, in this case, 2.028), and the rejection region foran F-test on this model. What would your conclusion be?

(5 Marks)

(g)

Why might we think a quadratic relationship between household size and electricityconsumption is appropriate? Calculate the turning point for household size, and discusswhether the quadratic term is significant (use the p-value). What does this imply about therelationship between electricity consumption and household size?

(6 Marks)

(h) Say we thought that smart meters might have a different effect on electricity consumptiondepending on where the household is located. How might we account for this in the model?

(2 Marks)

(i) What is the predicted electricity consumption of a suburban household with five individuals,an annual income of $80,000, three TVs and no smart metre installed? If you calculated a

prediction interval for a specific household with these characteristics, and a predictioninterval for an average household with the same characteristics, which interval would belarger? Explain your answer and give example of a factor that might cause the relevantinterval to be larger.

(5 Marks)

(j)

Give an intuitive explanation of what is meant by least squaresin a regression context.

(2 Marks)

Question 3 (40 marks)

(a) In the context of demography:

(i)

In studying a population the number of males and females aged under 1 from year to

year is a reflection of what rate?

(1 mark)

(ii)

As a population ages the number of males and females at each age changes as a result

of which two main factors?(1 mark)

(iii) Below is a population pyramid for males and females in Country X for the year 1975.

In interpreting the features of this pyramid

a. What may have happened in the 1941-1945 period?

b.

What does the size of the age group 25 to 29 indicate?

c.

What appears to have been constant for the last 10 to 15 years?

NoteTo construct the table male numbers are entered as negatives. The differences

for each age group between male and female numbers would normally be 105 males

for 100 females at ages under 20 with this ratio decreasing slowly to about age 70 then

reducing more significantly.

(3 marks)


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Age

Group

M

'000s

Fem

'000s Country X Population 19750-4 -180 171

5-9 -179 170

10-14 -179 170

15-19 -185 176

20-24 -198 189

25-29 -190 183

30-34 -135 131

35-39 -175 171

40-44 -172 171

45-49 -170 180

50-54 -160 180

55-59 -140 174

60-64 -138 158

65-69 -120 140

70-74 -115 123

75-79 -72 90

80-84 -53 70

85-89 -45 65

90-94 -30 45

95+ -15 35-200 -100 0 100 200

0-4

5-9

10-14

15-19

20-24

25-29

30-34

35-39

40-44

45-49

50-54

55-59

60-64

65-69

70-74

75-79

80-84

85-89

90-94

95+M '000s

Fem '000s


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(b) Attached is a condensed extract from the Australian Life Tables 2007-2009 published by theAustralian Bureau of Statistics in November 2010. Using that table answer the following:

(i) What is the probability that a 20 year old male survives to age 60 (to 2 decimal placesper cent)?

(1 mark)

(ii) If dxis the number of deaths at attained age x what is the value for females of (d16+d17+ d18)?

(1 mark)

(iii) What does exas listed in the 4thcolumn for each sex represent (both the name for this

entity and its meaning or interpretation)?(1 mark)

(iv)

For males age 50 now, if I was to say 50% of them will probably die before age Yand

50% after age Y. Using the tables what age is Yyears? (1 mark)

(v) A man aged 25 marries a woman aged 20. If probabilities of death are independent andin accordance with the life table what is the probability (to 2 decimal places per cent)that they will celebrate their 40thwedding anniversary together (assuming no divorce)?

(2 marks)

(vi)

In answering part (v) what property of the population is being assumed to apply for thenext 40 years that allows us to use the life table to predict ahead?

(1 mark)

(c) In the city of Oldville some 30% of car drivers are classified as young and 70% areclassified as old. The probability of a young driver having a car accident is 0.20 and the

probability of an old driver having a car accident is 0.05. We have the following probabilityfrequency table

Young (Y) Old (nY) All

Accident (A) .3 x .2 = .06 .7 x .05 = .035 .095

Claim free (nA) .3 x .8 = .24 .7 x .95 = .665 .905

Total .30 .70 1.000

(i) What type of probabilities are the cells with the values .06, .035, .24 and .665?

(1 mark)

(ii) What type of probabilities are the cells with the values of .095, .905, .30 and .70?(1 mark)

(iii)

Bayes Theorem says Pr (Y/A) = (Prob Item X) x Pr (Y) / Pr (A). What is Prob Item Xin this theorem and what type of probability is it?

(1 mark)

(iv)

Given Bayes Theorem calculate Pr (Y/A) as a % to 1 decimal place.(1 mark)


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(d) Using compound interest:

(i)

If nominal interest of 18% per annum is paid monthly, what is the effective interestrate (to 2 decimal places per cent)?

(1 mark)

(ii)

Joes father promises to pay him $5,000 in 3 years time. If Joe works on a 5% paeffective rate of interest in valuing the payment what present value would Joe put onthe promise (to nearest cent)?

(1 mark)

(iii)

$1,000 is invested in a term deposit for 2 years at 6% per annum interest with Bank Awhich pays interest annually. On maturity it is re-invested with Bank B for 2 years at8% per annum nominal rate. Bank B actually pays interest quarterly. What is the finalmaturity amount (to nearest cent).

(2 marks)

(iv)

A life office offers a 3 year insurance policy with a life sum insured of $1000 payableat the end of the year of death if death occurs during the 3 years and a survival payoutof $500 for the survivors at the end of the 3 years. The probability of death each year isq. The payments are valued at compound interest effective rate iper annum.

a) Using vi.e. 1/(1+i) and qin the expression write out a formula for the up-frontpremium for the contract. (Hintallow for probability of surviving each year)

(3 marks)

b) If the rate of interestiis 6% and the probability of death is 10% pa calculate theup-front premium. (Determine the premium for death and survival benefits

separately, and then quote the total)(5 marks)

(e) In the context of actuarial studies:

(i) A life insurance actuary would refer to a payment depending on the outcome of an

uncertain event as a ....... payment complete.

(1 mark)

(ii) Car Insurance Company A has 500 insured policyholders. Car Insurance Company B

has 5,000 insured policyholders. Comment briefly on the relative risks each insurerfaces with the change in the distribution of their claims from year to year.

(2 marks)

(iii) What are the main ways an Actuary of a General Insurance Company in Australia

would protect the Company against the adverse financial effects of large claims like

fire and flood catastrophes, or war risks?

(2 marks)


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(f) You are a General Insurance Actuary doing claim analysis for a company providing carinsurance

(i) The Managing Director asks you to review the reinsurance arrangements for the carinsurance company. Explain briefly why you would investigate the upper tail of thedistribution used for estimating claim size.

(1 mark)

(ii)You need to do some what-if scenario analysis on various possible outcomes for thecompany but your past claims data is scanty. Explain briefly how probabilitydistributions could be useful in this situation.

(1 mark)

(iii)Explain how in doing a claim analysis it may be useful in the same project to use botha binomial distribution and a normal distribution to analyse the same set of claim data.

(2 marks)

(g) If a probability distribution is expressed by the formula:

(i) What distribution is being referred to, and is it discrete or continuous?(1 mark)

(ii)

What does mean in the formula?

(1 mark)

(iii) What does x mean in the formula?

(1 mark)

exp !xf x x


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**** End of Examination ****

ETC1010_2011_S2 Exam Questions All Topics

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