# Module Information

#### Course Delivery

Delivery Type | Delivery length / details |
---|---|

Lecture | 22 Hours. (22 x 1 hour lectures) |

Seminars / Tutorials | 6 Hours. (6 x 1 hour example classes) |

#### Assessment

Assessment Type | Assessment length / details | Proportion |
---|---|---|

Semester Exam | 2 Hours (written examination) | 100% |

Supplementary Assessment | 2 Hours (written examination) | 100% |

### Learning Outcomes

On completion of this module, a student should be able to:

1. categorise, summarise and interpret various types of data;

2. explain the concept of probability;

3. deduce probabilities in a variety of simple symmetric situations;

4. solve elementary combinatoric problems;

5. explain the concept of random variable;

6. explain the concept of probability distribution and density;

7. describe a variety of standard distributions;

8. use probability tables or a calculator for finding probabilities associated with a variety of standard distributions;

9. deduce important 'features' of some standard distributions;

10. model stochastic situations with standard distributions;

11. explain the concepts of expectation, variance and standard deviation and deduce them in familiar standard and simple unfamiliar situations;

12. manipulate simple expressions involving expectations;

13. explain the Central Limit Theorem and its significance;

14. determine when it is appropriate to approximate a Binomial distribution by a Normal distribution and do this using the 'continuity correction'.

### Brief description

This module starts with the descriptive statistics used for summarising and displaying data. It then introduces probability, the mathematical language of uncertainty and discusses the analysis of data in commonly occurring situations.

### Aims

To introduce students to basic ways of thinking about data. To give students the methodology for summarising and interpreting data. To introduce the basic ideas of probability, random variable, probability distributions, expectation and variance.

### Content

2. PROBABILITY: Axioms of probability, deduction in symmetric situations, classical sample space.

3. COMBINATORICS: Basic formulae with applications.

4. THE ALGEBRA OF SETS: Basic formulae with applications.

5. CONDITIONAL PROBABILITY: Definition, the chain rule, Bayes rule, applications.

6. PROBABILITY DISTRIBUTIONS: Discrete and continuous cases, the probability mass function, the density function, calculation of probabilities, distribution functions, standard distributions, use in modelling. Calculation of probabilities using Statistical Tables.

7. EXPECTATION: Definitions of expectation, variance and standard deviation; properties, calculation in specific cases.

8. THE CENTRAL LIMIT THEOREM: Statement, significance, applications, approximation of the Binomial distribution by the Normal distribution.

[Note: concepts and methodology are illustrated throughout by means of a wide variety of specific examples.]

### Notes

This module is at CQFW Level 4