CIE A LEVEL STATISTICS 2 2nd EDITION BOOK AND WEBSITE LINK

Table of contents

Syllabus matching grid; 1 The Poisson distribution; 1.1 Introducing the Poisson distribution; 1.2 The role of the parameter of the Poisson distribution; 1.3 The recurrence relation for the Poisson distribution; 1.4 Mean and variance of the Poisson distribution; 1.5 Modelling with the Poisson distribution; 2 Approximations involving the Poisson distribution; 2.1 Poisson as an approximation to the Binomial; 2.2 The Normal approximation to the Poisson distribution; 3 Linear combination of random variables; 3.1 Expectation and variance of a linear function of a random variable; 3.2 Linear combination of two (or more) independent random variables; 3.3 Expectation and variance of a sum of repeated independent observations of a random variable, and the mean of those observations; 3.4 Comparing the sum of repeated independent observations with the multiple of a single observation; Review exercise A; Maths in real-life: The mathematics of the past; 4 Linear combination of Poisson and Normal variables; 4.1 The distribution of the sum of two independent Poisson random variables; 4.2 Linear functions and combinations of normal random variables; 5 Continuous random variables; 5.1 Introduction to continuous random variables; 5.2 Probability density functions; 5.3 Mean and variance of a continuous random variable; 5.4 Mode of a continuous random variable; 6 Sampling; 6.1 Populations, census and sampling; 6.2 Advantages and disadvantages of sampling; 6.3 Variability between samples and use of random numbers; 6.4 The sampling distribution of a statistic; 6.5 Sampling distribution of the mean of repeated observations of a random variable; 6.6 Sampling distribution of the mean of a sample from a normal distribution; 6.7 The Central Limit Theorem; 6.8 Descriptions of some sampling methods; Review exercise B; Maths in real-life: Modelling statistics; 7 Estimation; 7.1 Interval estimation; 7.2 Unbiased estimate of the population mean; 7.3 Unbiased estimate of the population variance; 7.4 Confidence intervals for the mean of a Normal distribution; 7.5 Confidence intervals for the mean of a large sample from any distribution; 7.6 Confidence intervals for a proportion; 8 Hypothesis testing for discrete distributions; 8.1 The logical basis for hypothesis testing; 8.2 Critical region; 8.3 Type I and Type II errors; 8.4 Hypothesis test for the proportion p of a Binomial distribution; 8.5 Hypothesis test for the mean of a Poisson distribution; 9 Hypothesis testing using the Normal distribution; 9.1 Hypothesis test for the mean of a Normal distribution; 9.2 Hypothesis test for the mean using a large sample; 9.3 Using a confidence interval to carry out a hypothesis test; Review exercise C; Maths in real-life: A risky business; List of formulae; Answers; Glossary of terms; Index