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T2187 Business analytics, applied modelling and prediction
创建日期：2024-08-06 14:38:10
标签： T2187
Business analytics, applied modelling and prediction

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T2187 Business analytics, applied modelling and prediction

Important note

 The format and structure of the examination may change in future years,

and any such changes will be publicised on the virtual learning environment (VLE).

Information about the subject guide and the Essential reading

references

Unless otherwise stated, all cross-references will be to the latest version of the course (2019). You

should always attempt to use the most recent edition of any Essential reading textbook, even if the

commentary and/or online reading list and/or subject guide refer to an earlier edition. If different

editions of Essential reading are listed, please check the VLE for reading supplements – if none are

available, please use the contents list and index of the new edition to find the relevant section.

General remarks

Learning outcomes

At the end of the course and having completed the essential reading and activities you should be

able to:

apply modelling at varying levels to aid decision-making

understand basic principles of how to analyse complex multivariate datasets with the aim of

extracting the important message contained within the large amount of data which is often

available

demonstrate the wide applicability of mathematical models while, at the same time,

identifying their limitations and possible misuse.

Format of the examination

The examination is two hours long and you must answer four questions out of five. The examination

is worth 70% of the final grade. The other 30% is determined by the coursework component. (The

coursework comprised a freestyle data visualisation project using Tableau, requiring the design of a

five-dashboard story and accompanying report – see the ‘Assessment’ section in the VLE for details.)

Overall performance

The performance of candidates in the examination was very pleasing, with many excellent answers.

Use of Excel is not directly examined, rather some questions required the interpretation of Excel

1

ST2187 Business analytics, applied modelling and prediction

output and/or formulae. Some answers lacked sufficient depth of explanation – remember to

comment in detail on each argument of a function.

Although this is an applied statistics course, candidates are reminded that commercial insight is also

important. Always think about which business decisions could be taken as a consequence of the

analysis, justifying the decision(s) based on the results – the course is about business analytics after

all!

Examination revision strategy

Many candidates are disappointed to find that their examination performance is poorer than they

expected. This may be due to a number of reasons, but one particular failing is ‘question

spotting’, that is, confining your examination preparation to a few questions and/or topics which

have come up in past papers for the course. This can have serious consequences.

We recognise that candidates might not cover all topics in the syllabus in the same depth, but you

need to be aware that examiners are free to set questions on any aspect of the syllabus. This

means that you need to study enough of the syllabus to enable you to answer the required number of

examination questions.

The syllabus can be found in the Course information sheet available on the VLE. You should read

the syllabus carefully and ensure that you cover sufficient material in preparation for the

examination. Examiners will vary the topics and questions from year to year and may well set

questions that have not appeared in past papers. Examination papers may legitimately include

questions on any topic in the syllabus. So, although past papers can be helpful during your revision,

you cannot assume that topics or specific questions that have come up in past examinations will

occur again.

If you rely on a question-spotting strategy, it is likely you will find yourself in difficulties

when you sit the examination. We strongly advise you not to adopt this strategy.

2

Examiners’ commentaries 2020

Examiners’ commentaries 2020

ST2187 Business analytics, applied modelling and prediction

Important note

This commentary reflects the examination and assessment arrangements for this course in the

academic year 2019–20. The format and structure of the examination may change in future years,

and any such changes will be publicised on the virtual learning environment (VLE).

Information about the subject guide and the Essential reading

references

Unless otherwise stated, all cross-references will be to the latest version of the course (2019). You

should always attempt to use the most recent edition of any Essential reading textbook, even if the

commentary and/or online reading list and/or subject guide refer to an earlier edition. If different

editions of Essential reading are listed, please check the VLE for reading supplements – if none are

available, please use the contents list and index of the new edition to find the relevant section.

Comments on specific questions

Candidates should answer FOUR of the following FIVE questions. All questions carry equal marks.

Question 1

(a) Consider a modified version of the Monty Hall problem. In this version, there

are 8 boxes, of which 1 box contains the prize and the other 7 boxes are empty.

You select one box at first. Monty, who knows where the prize is, then opens 6

of the remaining 7 boxes, all of which are shown to be empty. If Monty has a

choice of which boxes to open (i.e. if the prize is in the box you chose at first),

he will choose at random which one of the boxes to leave unopened.

i. Suppose that you have chosen Box 1, and then Monty opens Boxes 3 to 8,

leaving Box 2 unopened. After we have observed this, what is the probability

that the prize is in Box 1, and what is the probability that it is in Box 2?

(10 marks)

ii. How should a risk-neutral decision-maker use the probabilities computed in i.

to inform their strategy?

(3 marks)

Reading for this question

Block 1 on the VLE covers the Monty Hall problem as part of decision-making under

uncertainty.

3

ST2187 Business analytics, applied modelling and prediction

Approaching the question

i. Let Bj denote the event that the prize is in Box j, for j = 1, 2, . . . , 8, and let N2 denote

the event that Monty does not open Box 2. Bayes’ theorem tells us that the conditional

probability that the prize is in Box 1 is:

P (B1 |N2) = P (N2 |B1)P (B1)8∑

j=1

P (N2 |Bj)P (Bj)

=

P (N2 |B1)P (B1)

P (N2 |B1)P (B1) + P (N2 |B2)P (B2) +

8∑

j=3

P (N2 |Bj)P (Bj)

.

According to the rules of the game, the probabilities to use here are:

? P (B1) = P (B2) = · · · = P (B8) = 1/8, since all the boxes are initially equally likely to

contain the prize.

? P (N2 |B1) = 1/7. If the prize is in Box 1, Monty has a choice, so he chooses at

random which of the remaining boxes to leave unopened.

? P (N2 |B2) = 1. If the prize is in Box 2, Monty must leave it unopened.

? P (N2 |Bj) = 0 for j = 3, 4, . . . , 8. If the prize is in either Box 3 to 8, Monty cannot

open that box. This means that he must open all the other boxes not chosen by you,

including Box 2.

Therefore, the conditional probabilities are:

P (B1 |N2) = 1/7× 1/8

1/7× 1/8 + 1× 1/8 + 6× (0× 1/8) =

1

8

and P (B2 |N2) = 7/8. Hence you have an 87.5% chance of winning the prize if you

switch to Box 2.

ii. While neither conditional probability computed in i. offers certainty, a risk-neutral

decision-maker would ‘play to the probabililties’ and choose the strategy to always switch

to the unopened box, since a long-run expected win rate of 87.5% by switching is far

better than a long-run expected win rate of 12.5% by not switching.

(b) ‘If there is uncertainty about some monetary outcome and you are concerned

about return and risk, then all you need to see are the mean and standard

deviation. The entire distribution provides no extra useful information.’ Do you

agree or disagree? Provide an example to back up your argument.

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