Rövid leírás:
Providing complete syllabus support (9709), this stretching and practice-focused course builds the advanced skills needed for the latest Cambridge assessments and the transition to higher education. Engaging, real world examples make mathematics relevant to real life.
Több
Hosszú leírás:
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.
Több
Tartalomjegyzék:
Syllabus matching grid
1 The Poisson distribution
Introducing the Poisson distribution
The role of the parameter of the Poisson distribution
The recurrence relation for the Poisson distribution
Mean and variance of the Poisson distribution
Modelling with the Poisson distribution
2 Approximations involving the Poisson distribution
Poisson as an approximation to the Binomial
The Normal approximation to the Poisson distribution
3 Linear combination of random variables
Expectation and variance of a linear function of a random variable
Linear combination of two (or more) independent random variables
Expectation and variance of a sum of repeated independent observations of a random variable, and the mean of those observations
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
The distribution of the sum of two independent Poisson random variables
Linear functions and combinations of normal random variables
5 Continuous random variables
Introduction to continuous random variables
Probability density functions
Mean and variance of a continuous random variable
Mode of a continuous random variable
6 Sampling
Populations, census and sampling
Advantages and disadvantages of sampling
Variability between samples and use of random numbers
The sampling distribution of a statistic
Sampling distribution of the mean of repeated observations of a random variable
Sampling distribution of the mean of a sample from a normal distribution
The Central Limit Theorem
Descriptions of some sampling methods
Review exercise B
Maths in real-life: Modelling statistics
7 Estimation
Interval estimation
Unbiased estimate of the population mean
Unbiased estimate of the population variance
Confidence intervals for the mean of a Normal distribution
Confidence intervals for the mean of a large sample from any distribution
Confidence intervals for a proportion
8 Hypothesis testing for discrete distributions
The logical basis for hypothesis testing
Critical region
Type I and Type II errors
Hypothesis test for the proportion p of a Binomial distribution
Hypothesis test for the mean of a Poisson distribution
9 Hypothesis testing using the Normal distribution
Hypothesis test for the mean of a Normal distribution
Hypothesis test for the mean using a large sample
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
