1 Sampling; 1.1 Terms and notation; 1.2 Sampling; 1.3 Sampling techniques; 2 Continuous random variables; 2.1 Probability density function; 2.2 Mean and variance; 2.3 The median; 2.4 The mode; 2.5 The uniform (rectangular) distribution; 3 Hypothesis testing using the binomial distribution; 3.1 Defining terms; 3.2 Hypothesis testing checklist; 3.3 Choosing the significance level; 3.4 Critical values and critical (rejection) regions 3.5 One-tailed and two-tailed tests3.6 Type I and Type II errors; 4 Hypothesis testing and confidence intervals using the normal distribution; 4.1 Interpreting sample data using the normal distribution; 4.2 The Central Limit Theorem; 4.3 Confidence intervals; 4.4 How large a sample do you need?; 4.5 Confidence intervals for a proportion; 5 The Poisson distribution; 5.1 The Poisson distribution; 5.2 Modelling with a Poisson distribution; 5.3 The sum of two or more Poisson distributions; 5.4 The Poisson approximation to the binomial distribution 5.5 Using the normal distribution as an approximation for the Poisson distribution5.6 Hypothesis test for the mean of a Poisson distribution; 6 Linear combinations of random variables; 6.1 The expectation (mean) of a function of X, E(g[X); 6.2 Expectation: algebraic results; 6.3 The sums and differences of independent random variables; 6.4 More than two independent random variables
The Cambridge International AS & A Level Mathematics: Probability & Statistics 2 Coursebook (ISBN: 9781510421776) is tailored to the Cambridge International A Level Mathematics (9709) syllabus, focusing on advanced statistical concepts. It covers topics such as hypothesis testing, Poisson distribution, linear combinations of random variables, continuous random variables, and sampling. Designed for students aiming to enhance their statistical reasoning and prepare for examinations, this resource also emphasizes real-world applications of mathematics.