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- 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
| Erscheinungsjahr: | 2018 |
|---|---|
| Fachbereich: | Wahrscheinlichkeitstheorie |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Inhalt: | Bundle |
| ISBN-13: | 9780198425175 |
| ISBN-10: | 0198425171 |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: | Nicholson, James |
| Hersteller: | Oxford University Press |
| Maße: | 190 x 245 x 16 mm |
| Von/Mit: | James Nicholson |
| Erscheinungsdatum: | 12.07.2018 |
| Gewicht: | 0,478 kg |
- 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
| Erscheinungsjahr: | 2018 |
|---|---|
| Fachbereich: | Wahrscheinlichkeitstheorie |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Inhalt: | Bundle |
| ISBN-13: | 9780198425175 |
| ISBN-10: | 0198425171 |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: | Nicholson, James |
| Hersteller: | Oxford University Press |
| Maße: | 190 x 245 x 16 mm |
| Von/Mit: | James Nicholson |
| Erscheinungsdatum: | 12.07.2018 |
| Gewicht: | 0,478 kg |
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