Edexcel AS and A level Further Mathematics Further Statistics 1

Front Cover......Page 1
Contents......Page 4
Overarching themes......Page 5
Extra online content......Page 7
Chapter 1: Discrete random variables......Page 8
1.1: Expected value of a discrete random variable......Page 9
1.2: Variance of a discrete random variable......Page 12
1.3: Expected value and variance of a function of X......Page 14
1.4: Solving problems involving random variables......Page 18
Mixed exercise 1......Page 21
Summary of key points......Page 25
Chapter 2: Poisson distributions......Page 26
2.1: The Poisson distribution......Page 27
2.2: Modelling with the Poisson distribution......Page 30
2.3: Adding Poisson distributions......Page 34
2.4: Mean and variance of a Poisson distribution......Page 37
2.5: Mean and variance of the binomial distribution......Page 39
2.6: Using the Poisson distribution to approximate the binomial distribution......Page 41
Mixed exercise 2......Page 45
Summary of key points......Page 49
Chapter 3: Geometric and negative binomial distributions......Page 50
3.1: The geometric distribution......Page 51
3.2: Mean and variance of a geometric distribution......Page 54
3.3: The negative binomial distribution......Page 56
3.4: Mean and variance of the negative binomial distribution......Page 59
Mixed exercise 3......Page 62
Summary of key points......Page 64
Chapter 4: Hypothesis testing......Page 65
4.1: Testing for the mean of a Poisson distribution......Page 66
4.2: Finding critical regions for a Poisson distribution......Page 69
4.3: Hypothesis testing for the parameter p of a geometric distribution......Page 73
4.4: Finding critical regions for a geometric distribution......Page 76
Mixed exercise 4......Page 79
Summary of key points......Page 82
Chapter 5: Central limit theorem......Page 83
5.1: The central limit theorem......Page 84
5.2: Applying the central limit theorem to other distributions......Page 87
Mixed exercise 5......Page 89
Summary of key points......Page 91
Review exercise 1......Page 92
Chapter 6: Chi-squared tests......Page 98
6.1: Goodness of fit......Page 99
6.2: Degrees of freedom and the chi-squared family of distributions......Page 103
6.3: Testing a hypothesis......Page 106
6.4: Testing the goodness of fit with discrete data......Page 110
Testing a discrete uniform distribution as a model......Page 111
Testing a binomial distribution as a model......Page 112
Testing a Poisson distribution as a model......Page 115
6.5: Using contingency tables......Page 120
Degrees of freedom......Page 121
6.6: Apply goodness-of-fit tests to geometric distributions......Page 126
Mixed exercise 6......Page 129
Summary of key points......Page 134
Chapter 7: Probability generating functions......Page 135
7.1: Probability generating functions......Page 136
7.2: Probability generating functions of standard distributions......Page 139
7.3: Mean and variance of a distribution......Page 142
7.4: Sums of independent random variables......Page 146
Mixed exercise 7......Page 150
Summary of key points......Page 152
Chapter 8: Quality of tests......Page 153
8.1: Type I and Type II errors......Page 154
8.2: Finding Type I and Type II errors using the normal distribution......Page 160
8.3: Calculate the size and power of a test......Page 164
8.4: The power function......Page 169
Mixed exercise 8......Page 174
Summary of key points......Page 179
Review exercise 2......Page 180
Exam-style practice: AS......Page 187
Exam-style practice: A level......Page 189
Appendix......Page 192
Answers......Page 200
Index......Page 220