Mathematics; Probability & Statistics 2 - Goldie, Sophie (London, Hodder Education Group, 2018)
Endorsed by Cambridge Assessment International Education to provide full support for Paper 6 of the syllabus for examination from 2020. Take mathematical understanding to the next level with this accessible series, written by experienced authors, examiners and teachers. - Improve confidence as a mathematician with clear explanations, worked examples, diverse activities and engaging discussion points. - Advance problem-solving, interpretation and communication skills through a wealth of questions that promote higher-order thinking
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.
Keywords: Probability,Hypothesis; binomial distribution, poisson distribution