Science, Maths & Technology

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Modelling and estimation

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# Modelling and estimation

## Introduction

Please note: a Statement of Participation is not issued for this course.

Making sense of data, and hence obtaining useful and well-founded answers to important questions is the major goal of statistics. This free OpenLearn course, Modelling and estimation, is an extract from the Open University course M248 Analysing data [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] , a second level course that aims to bring you a wide-ranging, data-oriented presentation of many of the basic tools of modern practical statistics.

Modelling and estimation consists of selected material from M248, Books A and B. It has three sections in total. You should set aside about five hours to study each of the sections; the whole extract should take about 16 hours to study. The extract is a small part (around 8%) of a large course that is studied over eight months, and so can give only an approximate indication of the level and content of the full course.

In this extract you will learn about modelling and estimation using discrete data. The vast majority of the datasets used have arisen from real-world examples addressing real-world problems; this is typical of M248. It is relatively self-contained and should be reasonably easy to understand for someone with a good knowledge of basic mathematics. However, a few techniques and definitions are present in the extract without explanation.

Mathematical/statistical content at the Open University is usually provided to students in printed books, with PDFs of the same online. This format ensures that mathematical notation is presented accurately and clearly. The PDF of this extract thus shows the content exactly as it would be seen by an Open University student. However, the extract isn't entirely representative of the module materials, because there are no explicit references to use of the M248 software or to video material (although please note that the PDF may contain references to other parts of M248). In this extract, some illustrations have also been removed due to copyright restrictions.

Regrettably, mathematical and statistical content in PDF form is not accessible using a screenreader, and you may need additional help to read these documents.

Section 1 starts by defining probability, introduces relevant notation and briefly discusses basic properties of probabilities. The section concludes by considering some of the general features of and ideas about modelling discrete random variables.

Section 2 looks at one particular probability model for discrete data, the binomial distribution.

Section 3 investigates how data can be used to estimate the probability of success in a single Bernoulli trial and introduces maximum likelihood estimation.

This OpenLearn course is an adapted extract from the Open University course M248 Analysing data.