# Module ASB-2108:Probability and Optimisation

### Module Facts

10 Credits or 5 ECTS Credits

Semester 1

Organiser: Dr Chrysovalantis Vasilakis

### Overall aims and purpose

NOTE: This module is NOT available to students on BA degrees.

AIMS: To provide an introduction to probability and statistics.

### Course content

1. Partial differentiation, and optimisation of functions of two variables;
2. Integration;
3. Probability distributions and random variables;
4. Measures of central tendency and dispersion, mean and variance;
5. Discrete random variables, the Binomial and Poisson distributions;
6. Continuous random variables, the Normal distribution, and statistical tables;
7. Populations and samples, estimators and estimates;
8. Confidence intervals

### Assessment Criteria

#### threshold

Demonstration of the ability to perform simple probability manipulations and an understanding of basic statistical ideas to describe data and assess portfolios.

#### good

In addition to the above, more competence in the evaluation of probabilities, the ability to evaluate population and sample means and variances and other moments both from first principles and also with the aid of some summary measures.

#### excellent

In addition to the above, the ability to succinctly interpret the results and to demonstrate a clear understanding of all the assumptions underlying the analysis.

### Learning outcomes

1. Evaluate measures of central tendency and dispersion.

2. Identify the turning points of functions of two variables.

3. Solve constrained optimisation problems.

4. Integrate simple mathematical functions.

5. Evaluate probabilities involving the Binomial, Poisson and Normal distributions.

6. Evaluate classical confidence intervals for a population mean and variance, using statistical tables for the Normal, Chi-square and distributions.

### Assessment Methods

Type Name Description Weight
CLASS TEST Mid-term Test 25
EXAM Exam S1 2hrs 75

### Teaching and Learning Strategy

Hours
Lecture

One 2-hour lecture per week.

20
Tutorial

One 1-hour tutorial per fortnight.

4
Private study 76

### Transferable skills

• Numeracy - Proficiency in using numbers at appropriate levels of accuracy
• Computer Literacy - Proficiency in using a varied range of computer software
• Self-Management - Able to work unsupervised in an efficient, punctual and structured manner. To examine the outcomes of tasks and events, and judge levels of quality and importance
• Exploring - Able to investigate, research and consider alternatives
• Inter-personal - Able to question, actively listen, examine given answers and interact sensitevely with others
• Critical analysis & Problem Solving - Able to deconstruct and analyse problems or complex situations. To find solutions to problems through analyses and exploration of all possibilities using appropriate methods, rescources and creativity.
• Self-awareness & Reflectivity - Having an awareness of your own strengths, weaknesses, aims and objectives. Able to regularly review, evaluate and reflect upon the performance of yourself and others

### Subject specific skills

• Quantification and design. Data, and their effective organisation, presentation and analysis, are important in economics. The typical student will have some familiarity with the principal sources of economic information and data relevant to industry, commerce, society and government, and have had practice in organising it and presenting it informatively. This skill is important at all stages in the decision-making process.