Example Examination

Total Duration:              120 mins

ANSWER ALL FIVE QUESTIONS

Total marks: 60

Instructions for Candidates

• Begin each answer on a new page in the answer book.
• Examination materials must not be removed from the examination room.

Permitted Materials

• Calculators without transmission capabilities allowed.
• Foreign language paper dictionaries permitted.

DO NOT COMMENCE WRITING UNTIL INSTRUCTED TO DO SO

Question 1 – Probability and Entropy

Equation for Entropy given in the course, you may assume b is 2.

• A “fixed” 4-sided dice also have a 25% chance of showing each face, but the faces are labelled 1, 1, 3, and 5. What is the probability of showing a 1?

[1 mark]

• Use the entropy equation to provide the entropy of a fair dice that has an equal chance of showing each face. You must show your working.

[3 marks]

• The DNA of living things is made up of nucleotides. Each sugar in a nucleotide has a nitrogen base attached to it. There are four different types of nitrogen bases found in DNA. They include adenine (A), cytosine (C), guanine (G), and thymine (T). In standard humans, these occur roughly equally. You tinker a little and produce a human which has A:C:G:T in ratios 1:6:3:5. What is the entropy of a random variable that models this? Show your working.

[4 marks]

• You have 3 green balls and 4 red balls in a jar. You pick two balls from the jar without looking. What is the probability that you picked a red ball first, then a green ball?

[4 marks] [Total marks for Question 1: 12 marks]

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Question 2 – SQL and Normalisation

• What will be displayed if we entered the SQL command “SELECT * FROM FEE;”.

[2 marks]

• What is the full outer join of these relations?

[4 marks]

• What is the result of an INNER JOIN on the ID attribute between the tables shown above?

[4 marks]

• Why have the fees been separated from the student data? Explain in terms of normalisation.

[4 marks]

[Total marks for Question 2: 12 marks]

Question 3 – Indexing and Storage

• What is the possible advantage if an individual database record can fit within one page?

[2 marks]

• You have an unsorted file storage for 100 records. If it takes 1 second to examine each record, how long, on average, will it take to find a record that is there?

[2 marks]

• Give examples of three different forms of index and describe them?

[2 marks]

• You are writing an index for a cookbook and want to write a program that will make it easy find all of the recipes that use avocadoes. What sort of index do you think you would use to do it efficiently? Explain your answer.

[2 marks]

• You have 40,000 distinct words to index and your blocking factor is 50 index entries per block, which is also your fan-out. How many levels will your multilevel index have and which level is the top?

[4 marks]

[Total marks for Question 3: 12 marks]

Question 4 – Trees and Entity-Relationship Diagrams

• What string is produced if you traverse the tree above in pre-order traversal?

[2 marks]

• Is the tree shown above a balanced tree? Explain your answer.

[2 marks]

• Draw the entity-relationship (ER) diagram for a model that has entities ANIMAL and FOOD and a relationship linking them called CAN_EAT. ANIMAL has the attribute SPECIES and FOOD has the attribute NAME.

[5 marks]

• Explain what “total participation” means in a relationship mean for an entity.

[3 marks]

[Total marks for Question 4: 12 marks]

Question 5 – Ethics, Knowledge and Security

• Your web-based business is located in America, but you do extensive business with firms in London. Are you liable to the provisions of the GDPR?

[2 marks]

• A well-known study of Parole Board judges found that judges were less likely to grant parole when they were tired or hungry. What is this an example of? How could you ensure that this issue did not unfairly affect one group of people disproportionately?

[2 marks]

• Your postcode storage system has a configuration error and accidentally leaks the third digit of the stored postcode, along with the initials of the people who your system has associated with that postcode. How would you determine the significance of this leakage?

[4 marks]

• What is a Zero-Knowledge Proof? Explain why the Magic Cave’s zero-knowledge properties could be affected by two factors: firstly, that the verifier stands at the junction and observes which tunnel the prover takes and, secondly, that the verifier flips a coin to choose which tunnel the prover is to emerge from. Hint: remember the three conditions for a Zero-Knowledge Proof.

[4 marks]

[Total marks for Question 5: 12 marks]

END OF EXAMINATION PAPER

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