Ebook: A Modern Introduction to Probability and Statistics: Understanding Why and How

Probability and Statistics are studied by most science students, usually as a second- or third-year course. Many current texts in the area are just cookbooks and, as a result, students do not know why they perform the methods they are taught, or why the methods work. The strength of this book is that it readdresses these shortcomings; by using examples, often from real-life and using real data, the authors can show how the fundamentals of probabilistic and statistical theories arise intuitively. It provides a tried and tested, self-contained course, that can also be used for self-study.

A Modern Introduction to Probability and Statistics has numerous quick exercises to give direct feedback to the students. In addition the book contains over 350 exercises, half of which have answers, of which half have full solutions. A website at www.springeronline.com/1-85233-896-2 gives access to the data files used in the text, and, for instructors, the remaining solutions. The only pre-requisite for the book is a first course in calculus; the text covers standard statistics and probability material, and develops beyond traditional parametric models to the Poisson process, and on to useful modern methods such as the bootstrap.

This will be a key text for undergraduates in Computer Science, Physics, Mathematics, Chemistry, Biology and Business Studies who are studying a mathematical statistics course, and also for more intensive engineering statistics courses for undergraduates in all engineering subjects.

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Probability and Statistics are studied by most science students, usually as a second- or third-year course. Many current texts in the area are just cookbooks and, as a result, students do not know why they perform the methods they are taught, or why the methods work. The strength of this book is that it readdresses these shortcomings; by using examples, often from real-life and using real data, the authors can show how the fundamentals of probabilistic and statistical theories arise intuitively. It provides a tried and tested, self-contained course, that can also be used for self-study.

A Modern Introduction to Probability and Statistics has numerous quick exercises to give direct feedback to the students. In addition the book contains over 350 exercises, half of which have answers, of which half have full solutions. A website at www.springeronline.com/1-85233-896-2 gives access to the data files used in the text, and, for instructors, the remaining solutions. The only pre-requisite for the book is a first course in calculus; the text covers standard statistics and probability material, and develops beyond traditional parametric models to the Poisson process, and on to useful modern methods such as the bootstrap.

This will be a key text for undergraduates in Computer Science, Physics, Mathematics, Chemistry, Biology and Business Studies who are studying a mathematical statistics course, and also for more intensive engineering statistics courses for undergraduates in all engineering subjects.

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Probability and Statistics are studied by most science students, usually as a second- or third-year course. Many current texts in the area are just cookbooks and, as a result, students do not know why they perform the methods they are taught, or why the methods work. The strength of this book is that it readdresses these shortcomings; by using examples, often from real-life and using real data, the authors can show how the fundamentals of probabilistic and statistical theories arise intuitively. It provides a tried and tested, self-contained course, that can also be used for self-study.

A Modern Introduction to Probability and Statistics has numerous quick exercises to give direct feedback to the students. In addition the book contains over 350 exercises, half of which have answers, of which half have full solutions. A website at www.springeronline.com/1-85233-896-2 gives access to the data files used in the text, and, for instructors, the remaining solutions. The only pre-requisite for the book is a first course in calculus; the text covers standard statistics and probability material, and develops beyond traditional parametric models to the Poisson process, and on to useful modern methods such as the bootstrap.

This will be a key text for undergraduates in Computer Science, Physics, Mathematics, Chemistry, Biology and Business Studies who are studying a mathematical statistics course, and also for more intensive engineering statistics courses for undergraduates in all engineering subjects.

Content:
Front Matter....Pages I-XV
Why probability and statistics?....Pages 1-11
Outcomes, events, and probability....Pages 13-24
Conditional probability and independence....Pages 25-40
Discrete random variables....Pages 41-55
Continuous random variables....Pages 57-70
Simulation....Pages 71-87
Expectation and variance....Pages 89-102
Computations with random variables....Pages 103-114
Joint distributions and independence....Pages 115-134
Covariance and correlation....Pages 135-150
More computations with more random variables....Pages 151-166
The Poisson process....Pages 167-179
The law of large numbers....Pages 181-194
The central limit theorem....Pages 195-205
Exploratory data analysis: graphical summaries....Pages 207-230
Exploratory data analysis: numerical summaries....Pages 231-243
Basic statistical models....Pages 245-268
The bootstrap....Pages 269-284
Unbiased estimators....Pages 285-297
Efficiency and mean squared error....Pages 299-311
Maximum likelihood....Pages 313-327
The method of least squares....Pages 329-340
Confidence intervals for the mean....Pages 341-360
More on confidence intervals....Pages 361-371
Testing hypotheses: essentials....Pages 373-382
Testing hypotheses: elaboration....Pages 383-397
The t-test....Pages 399-413
Comparing two samples....Pages 415-428
Back Matter....Pages 429-486

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Probability and Statistics are studied by most science students, usually as a second- or third-year course. Many current texts in the area are just cookbooks and, as a result, students do not know why they perform the methods they are taught, or why the methods work. The strength of this book is that it readdresses these shortcomings; by using examples, often from real-life and using real data, the authors can show how the fundamentals of probabilistic and statistical theories arise intuitively. It provides a tried and tested, self-contained course, that can also be used for self-study.

A Modern Introduction to Probability and Statistics has numerous quick exercises to give direct feedback to the students. In addition the book contains over 350 exercises, half of which have answers, of which half have full solutions. A website at www.springeronline.com/1-85233-896-2 gives access to the data files used in the text, and, for instructors, the remaining solutions. The only pre-requisite for the book is a first course in calculus; the text covers standard statistics and probability material, and develops beyond traditional parametric models to the Poisson process, and on to useful modern methods such as the bootstrap.

This will be a key text for undergraduates in Computer Science, Physics, Mathematics, Chemistry, Biology and Business Studies who are studying a mathematical statistics course, and also for more intensive engineering statistics courses for undergraduates in all engineering subjects.

Content:
Front Matter....Pages I-XV
Why probability and statistics?....Pages 1-11
Outcomes, events, and probability....Pages 13-24
Conditional probability and independence....Pages 25-40
Discrete random variables....Pages 41-55
Continuous random variables....Pages 57-70
Simulation....Pages 71-87
Expectation and variance....Pages 89-102
Computations with random variables....Pages 103-114
Joint distributions and independence....Pages 115-134
Covariance and correlation....Pages 135-150
More computations with more random variables....Pages 151-166
The Poisson process....Pages 167-179
The law of large numbers....Pages 181-194
The central limit theorem....Pages 195-205
Exploratory data analysis: graphical summaries....Pages 207-230
Exploratory data analysis: numerical summaries....Pages 231-243
Basic statistical models....Pages 245-268
The bootstrap....Pages 269-284
Unbiased estimators....Pages 285-297
Efficiency and mean squared error....Pages 299-311
Maximum likelihood....Pages 313-327
The method of least squares....Pages 329-340
Confidence intervals for the mean....Pages 341-360
More on confidence intervals....Pages 361-371
Testing hypotheses: essentials....Pages 373-382
Testing hypotheses: elaboration....Pages 383-397
The t-test....Pages 399-413
Comparing two samples....Pages 415-428
Back Matter....Pages 429-486
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