Module Identifier MA11310 Module Title STATISTICS Academic Year 2001/2002 Co-ordinator Mr David Jones Semester Semester 2 Pre-Requisite MA10310 Mutually Exclusive May not be taken at the same time as MA13510 Course delivery Lecture 20 x 1 hour lectures Seminars / Tutorials 5 x 1 hour tutorials Workshop 2 x 1 hour workshops (including test) Assessment Continuous assessment 25% Exam 2 Hours (written examination) 75% Resit assessment 2 Hours (written examination) 100%

#### General 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.

#### Learning outcomes

On completion of this module, a student should be able to:
• describe the notion of covariance;
• calculate means and variances of linear combinations of random variables;
• identify a probability distribution appropriate to a given situation;
• describe modelling in terms of Bernoulli trials and of random events;
• manipulate distributions to obtain moments and to sketch curves;
• assess a given value in relation to the scale of a given probability distribution;
• estimate means and proportions from data;
• explain the use of a statistical test;
• construct and carry out simple tests.

#### Syllabus

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. The idea of likelihood.