Support achievement in the latest syllabus (9709), for examination from 2020, with a stretching, practice-driven approach that builds the advanced skills required for Cambridge exam success and progression to further study.
This new edition is fully aligned with the Probability & Statistics 2 part of the latest International AS & A Level syllabus, and contains a comprehensive mapping grid so you can be sure of complete support.
Get students ready for higher education with a focus on real world application. From parabolic reflectors to technology in sport, up-to-date, international examples show how mathematics is used in real life.
Students have plenty of opportunities to hone their skills with extensive graduated practice and thorough worked examples. Plus, give students realistic practice for their exams with exam-style questions covering every topic.
Answers are included in the back of the book with full step-by-step solutions for all exercises and exam-style questions available on the accompanying support site.
Complete Probability & Statistics 2 for Cambridge International AS & A Level
Description
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