# Module Information

Module Identifier
MA11310
Module Title
Statistics
2024/2025
Co-ordinator
Semester
Semester 2
Pre-Requisite
Exclusive (Any Acad Year)
Other Staff

#### Assessment

Assessment Type Assessment length / details Proportion
Semester Assessment Coursework  Mark based on attendance at lectures and tutorials and submitted assignments  20%
Semester Exam 2 Hours   (Written Examination)  80%
Supplementary Exam 2 Hours   (Written Examination)  100%

### Learning Outcomes

On completion of this module, a student should be able to:
1. describe the notion of covariance;
2. calculate means and variances of linear combinations of random variables;
3. identify a probability distribution appropriate to a given situation;
4. describe modelling in terms of Bernoulli trials and of random events;
5. manipulate distributions to obtain moments and to sketch curves;
6. assess a given value in relation to the scale of a given probability distribution;
7. estimate means and proportions from data;
8. explain the use of statistical tests and confidence intervals;
9. construct and carry out simple tests and confidence intervals;
10.use relevant statistical tables.

### Brief description

This module aims to develop common probability models, applicable to a variety of situations and to illustrate their use in statistical inference. It also includes an introduction to the theory of estimation.

### Aims

To introduce the subject of Statistics to mathematics students.

### Content

1. THE INFERENCE PROBLEM: The difference between probability and statistical inference. Assessing 'typical' values from a distribution. The idea of a statistic. Estimates and estimators. Accuracy and precision. Bias, sampling, variance and mean squared error. Comparison of estimators.
2. PROBABILISTIC (STOCHASTIC) MODELLING (INCLUDING EXAMPLES OF INFERENCE): Bernoulli trials and distributions based on them (Geometric, Binomial). Opinion polls. The ideas of covariance and correlation. Variances of linear combinations of random variables. Modelling random events. The Poisson and exponential distributions. Normality and the Central Limit Theorem. The Weak Law of Large Numbers.
3. INFERENCE: Sampling mean, sampling variance and standard deviation of a sample total and a sample average. Statistical testing. Tail areas. p-values. Examples of simple tests. The notion of a confidence interval.

### Module Skills

Skills Type Skills details
Adaptability and resilience Completion of tasks (assignments) to set deadlines will aid personal development.
Creative Problem Solving The assignments will give the students opportunities to show creativity in finding solutions and develop their problem solving skills.
Digital capability Use of Blackboard and internet resources.
Professional communication Written answers to exercises must be clear and well structured.
Subject Specific Skills Broadens exposure of students to topics in mathematics.

### Notes

This module is at CQFW Level 4