BOOK
Edexcel AS and A level Further Mathematics Further Statistics 1
(2017)
Additional Information
Book Details
Abstract
Exam Board: Edexcel
Level: AS and A level
Subject: Further Mathematics
First teaching: September 2017
First exams: Summer 2018
With over 1.3 million copies sold of the previous edition, Pearson’s textbooks are the market-leading and trusted resources for AS and A level Mathematics.
- Fully updated to match the new specifications, with more of a focus on problem- solving and modelling as well as supporting the large data set and new calculators.
- FREE additional online content to support independent learning, including full worked solutions for every question in the book (SolutionBank), GeoGebra interactives and support for the new calculators.
- Includes access to an online digital edition (valid for 3 years once activated).
- Includes worked examples with guidance, lots of exam-style questions, practice papers, and plenty of mixed and review exercises.
This book covers all the content needed for the optional Edexcel AS and A level Further Statistics 1 exams.
Table of Contents
| Section Title | Page | Action | Price |
|---|---|---|---|
| Front Cover | Front Cover | ||
| Contents | iii | ||
| Overarching themes | iv | ||
| Extra online content | vi | ||
| Chapter 1: Discrete random variables | 1 | ||
| 1.1: Expected value of a discrete random variable | 2 | ||
| 1.2: Variance of a discrete random variable | 5 | ||
| 1.3: Expected value and variance of a function of X | 7 | ||
| 1.4: Solving problems involving random variables | 11 | ||
| Mixed exercise 1 | 14 | ||
| Summary of key points | 18 | ||
| Chapter 2: Poisson distributions | 19 | ||
| 2.1: The Poisson distribution | 20 | ||
| 2.2: Modelling with the Poisson distribution | 23 | ||
| 2.3: Adding Poisson distributions | 27 | ||
| 2.4: Mean and variance of a Poisson distribution | 30 | ||
| 2.5: Mean and variance of the binomial distribution | 32 | ||
| 2.6: Using the Poisson distribution to approximate the binomial distribution | 34 | ||
| Mixed exercise 2 | 38 | ||
| Summary of key points | 42 | ||
| Chapter 3: Geometric and negative binomial distributions | 43 | ||
| 3.1: The geometric distribution | 44 | ||
| 3.2: Mean and variance of a geometric distribution | 47 | ||
| 3.3: The negative binomial distribution | 49 | ||
| 3.4: Mean and variance of the negative binomial distribution | 52 | ||
| Mixed exercise 3 | 55 | ||
| Summary of key points | 57 | ||
| Chapter 4: Hypothesis testing | 58 | ||
| 4.1: Testing for the mean of a Poisson distribution | 59 | ||
| 4.2: Finding critical regions for a Poisson distribution | 62 | ||
| 4.3: Hypothesis testing for the parameter p of a geometric distribution | 66 | ||
| 4.4: Finding critical regions for a geometric distribution | 69 | ||
| Mixed exercise 4 | 72 | ||
| Summary of key points | 75 | ||
| Chapter 5: Central limit theorem | 76 | ||
| 5.1: The central limit theorem | 77 | ||
| 5.2: Applying the central limit theorem to other distributions | 80 | ||
| Mixed exercise 5 | 82 | ||
| Summary of key points | 84 | ||
| Review exercise 1 | 85 | ||
| Chapter 6: Chi-squared tests | 91 | ||
| 6.1: Goodness of fit | 92 | ||
| 6.2: Degrees of freedom and the chi-squared family of distributions | 96 | ||
| 6.3: Testing a hypothesis | 99 | ||
| 6.4: Testing the goodness of fit with discrete data | 103 | ||
| Testing a discrete uniform distribution as a model | 104 | ||
| Testing a binomial distribution as a model | 105 | ||
| Testing a Poisson distribution as a model | 108 | ||
| 6.5: Using contingency tables | 113 | ||
| Setting the hypotheses | 114 | ||
| Selecting a model | 114 | ||
| Degrees of freedom | 114 | ||
| 6.6: Apply goodness-of-fit tests to geometric distributions | 119 | ||
| Mixed exercise 6 | 122 | ||
| Summary of key points | 127 | ||
| Chapter 7: Probability generating functions | 128 | ||
| 7.1: Probability generating functions | 129 | ||
| 7.2: Probability generating functions of standard distributions | 132 | ||
| 7.3: Mean and variance of a distribution | 135 | ||
| 7.4: Sums of independent random variables | 139 | ||
| Mixed exercise 7 | 143 | ||
| Summary of key points | 145 | ||
| Chapter 8: Quality of tests | 146 | ||
| 8.1: Type I and Type II errors | 147 | ||
| 8.2: Finding Type I and Type II errors using the normal distribution | 153 | ||
| 8.3: Calculate the size and power of a test | 157 | ||
| 8.4: The power function | 162 | ||
| Mixed exercise 8 | 167 | ||
| Summary of key points | 172 | ||
| Review exercise 2 | 173 | ||
| Exam-style practice: AS | 180 | ||
| Exam-style practice: A level | 182 | ||
| Appendix | 185 | ||
| Answers | 193 | ||
| Index | 213 |