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.
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.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
* 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
* 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
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