Edexcel AS and A Level Further Mathematics Further Statistics 2.pdf

Front Cover......Page 1
Contents......Page 4
Overarching themes......Page 5
Extra online content......Page 7
Chapter 1: Linear regression......Page 8
1.1: Least squares linear regression......Page 9
1.2: Residuals......Page 17
Mixed exercise: 1......Page 23
Chapter 2: Correlation......Page 28
2.1: The product moment correlation coefficient......Page 29
2.2: Spearman’s rank correlation coefficient......Page 33
2.3: Hypothesis testing for zero correlation......Page 40
Mixed exercise: 2......Page 45
Chapter 3: Continuous distributions......Page 51
3.1: Continuous random variables......Page 52
3.2: The cumulative distribution function......Page 58
3.3: Mean and variance of a continuous distribution......Page 63
3.4: Mode, median, percentiles and skewness......Page 70
3.5: The continuous uniform distribution......Page 78
3.6: Modelling with the continuous uniform distribution......Page 86
Mixed exercise: 3......Page 89
Chapter 4: Combinations ofrandom variables......Page 99
4.1: Combinations of random variables......Page 100
Review exercise: 1......Page 106
Chapter 5: Estimation, confidence intervals and tests usinga normal distribution......Page 116
5.1: Estimators, bias and standard error......Page 117
5.2: Confidence intervals......Page 127
5.3: Hypothesis testing for the difference between means......Page 134
5.4: Use of large sample results for an unknown population......Page 139
Mixed exercise: 5......Page 142
Chapter 6: Further hypothesis tests......Page 148
6.1: Variance of a normal distribution......Page 149
6.2: Hypothesis testing for the variance of a normal distribution......Page 153
6.3: The F-distribution......Page 156
6.4: The F-test......Page 162
Mixed exercise: 6......Page 166
Chapter 7: Confidence intervals and tests using the t-distribution......Page 170
7.1: Mean of a normal distribution with unknown variance......Page 171
7.2: Hypothesis test for the mean of a normal distribution with unknown variance......Page 177
7.3: The paired t-test......Page 181
7.4: Difference between means of two independent normal distributions......Page 187
7.5: Hypothesis test for the difference between means......Page 192
Mixed exercise: 7......Page 196
Review exercise: 2......Page 203
Exam-style practice paper (AS level)......Page 211
Exam-style practice paper (A level)......Page 213
Binomial cumulative distribution function......Page 216
Percentage points of the normal distribution......Page 221
Percentage points of the χ2 distribution......Page 222
Critical values for correlation coefficients......Page 223
Percentage points of Student’s t-distribution......Page 224
Percentage points of the F-distribution......Page 225
Poisson cumulative distribution function......Page 226
Formulae......Page 227
Answers......Page 232
Index......Page 263
Back Cover......Page 265