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E-raamat: Modern Introduction to Probability and Statistics: Understanding Why and How

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Modern Introduction to Probability and Statistics: Understanding Why and HowSuurem pilt
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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.

Probability and Statistics are studied by most science students. 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. This book readdresses these shortcomings; by using examples, often from real-life and using real data, the authors show how the fundamentals of probabilistic and statistical theories arise intuitively. There are numerous quick exercises to give direct feedback to students, and over 350 exercises, half of which have answers, of which half have full solutions. A website gives access to the data files used in the text, and, for instructors, the remaining solutions. The only prerequisite is a first course in calculus.

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From the reviews:



"[ the material is] superbly motivated with interest-grabbing examples... exercises excellent and plentiful." Edward Williams, University of Michigan-Dearborn, USA



"... it is a notoriously hard task to introduce probability and statistics with a mix of intuition and mathematics to keep students motivated. Therefore, I very much welcome this book and recommend it as course material." Sara van de Geer, Leiden University, The Netherlands 



"This textbook provides a well-written first course in probability and statistics...It is a book that has been written based on the long teaching experience of the authors and I would certainly recommend it for university coursework." Short Book Reviews of the International Statistical Institute,  December 2005



"This book has numerous quick exercises to give direct feedback to the students. A website at www.springeronline.com/978-1-85233-896-1 gives access to the data files used inthe text . 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." (Rainer Beedgen, Zentralblatt MATH, Vol. 1079, 2006)



"The book is designed for a one-semester introductory course in probability and statistics basics for engineering students. It can also be used by students in other more mathematically oriented majors such as applied mathematics with more emphasis on the mathematics and additional coverage in topics such as combinatorics, conditional expectation, and generating functions. More elaborate exercises and real datasets are given at the end of each chapter." (Arthur B. Yeh, Technometrics, Vol. 49 (3), August, 2007)

1 Why probability and statistics?
1(12)
1.1 Biometry: iris recognition
1(2)
1.2 Killer football
3(1)
1.3 Cars and goats: the Monty Hall dilemma
4(1)
1.4 The space shuttle Challenger
5(2)
1.5 Statistics versus intelligence agencies
7(2)
1.6 The speed of light
9(4)
2 Outcomes, events, and probability
13(12)
2.1 Sample spaces
13(1)
2.2 Events
14(2)
2.3 Probability
16(2)
2.4 Products of sample spaces
18(1)
2.5 An infinite sample space
19(2)
2.6 Solutions to the quick exercises
21(1)
2.7 Exercises
21(4)
3 Conditional probability and independence
25(16)
3.1 Conditional probability
25(2)
3.2 The multiplication rule
27(3)
3.3 The law of total probability and Bayes' rule
30(2)
3.4 Independence
32(3)
3.5 Solutions to the quick exercises
35(2)
3.6 Exercises
37(4)
4 Discrete random variables
41(16)
4.1 Random variables
41(2)
4.2 The probability distribution of a discrete random variable
43(2)
4.3 The Bernoulli and binomial distributions
45(3)
4.4 The geometric distribution
48(2)
4.5 Solutions to the quick exercises
50(1)
4.6 Exercises
51(6)
5 Continuous random variables
57(14)
5.1 Probability density functions
57(3)
5.2 The uniform distribution
60(1)
5.3 The exponential distribution
61(2)
5.4 The Pareto distribution
63(1)
5.5 The normal distribution
64(1)
5.6 Quantiles
65(2)
5.7 Solutions to the quick exercises
67(1)
5.8 Exercises
68(3)
6 Simulation
71(18)
6.1 What is simulation?
71(1)
6.2 Generating realizations of random variables
72(3)
6.3 Comparing two jury rules
75(5)
6.4 The single-server queue
80(4)
6.5 Solutions to the quick exercises
84(1)
6.6 Exercises
85(4)
7 Expectation and variance
89(14)
7.1 Expected values
89(4)
7.2 Three examples
93(1)
7.3 The change-of-variable formula
94(2)
7.4 Variance
96(3)
7.5 Solutions to the quick exercises
99(1)
7.6 Exercises
99(4)
8 Computations with random variables
103(12)
8.1 Transforming discrete random variables
103(1)
8.2 Transforming continuous random variables
104(2)
8.3 Jensen's inequality
106(2)
8.4 Extremes
108(2)
8.5 Solutions to the quick exercises
110(1)
8.6 Exercises
111(4)
9 Joint distributions and independence
115(20)
9.1 Joint distributions of discrete random variables
115(3)
9.2 Joint distributions of continuous random variables
118(4)
9.3 More than two random variables
122(2)
9.4 Independent random variables
124(1)
9.5 Propagation of independence
125(1)
9.6 Solutions to the quick exercises
126(1)
9.7 Exercises
127(8)
10 Covariance and correlation 135(16)
10.1 Expectation and joint distributions
135(3)
10.2 Covariance
138(3)
10.3 The correlation coefficient
141(2)
10.4 Solutions to the quick exercises
143(1)
10.5 Exercises
144(7)
11 More computations with more random variables 151(16)
11.1 Sums of discrete random variables
151(3)
11.2 Sums of continuous random variables
154(5)
11.3 Product and quotient of two random variables
159(3)
11.4 Solutions to the quick exercises
162(1)
11.5 Exercises
163(4)
12 The Poisson process 167(14)
12.1 Random points
167(1)
12.2 Taking a closer look at random arrivals
168(3)
12.3 The one-dimensional Poisson process
171(2)
12.4 Higher-dimensional Poisson processes
173(3)
12.5 Solutions to the quick exercises
176(1)
12.6 Exercises
176(5)
13 The law of large numbers 181(14)
13.1 Averages vary less
181(2)
13.2 Chebyshev's inequality
183(2)
13.3 The law of large numbers
185(3)
13.4 Consequences of the law of large numbers
188(3)
13.5 Solutions to the quick exercises
191(1)
13.6 Exercises
191(4)
14 The central limit theorem 195(12)
14.1 Standardizing averages
195(4)
14.2 Applications of the central limit theorem
199(3)
14.3 Solutions to the quick exercises
202(1)
14.4 Exercises
203(4)
15 Exploratory data analysis: graphical summaries 207(24)
15.1 Example: the Old Faithful data
207(2)
15.2 Histograms
209(3)
15.3 Kernel density estimates
212(7)
15.4 The empirical distribution function
219(2)
15.5 Scatterplot
221(4)
15.6 Solutions to the quick exercises
225(1)
15.7 Exercises
226(5)
16 Exploratory data analysis: numerical summaries 231(14)
16.1 The center of a dataset
231(2)
16.2 The amount of variability of a dataset
233(1)
16.3 Empirical quantiles, quartiles, and the IQR
234(2)
16.4 The box-and-whisker plot
236(2)
16.5 Solutions to the quick exercises
238(2)
16.6 Exercises
240(5)
17 Basic statistical models 245(24)
17.1 Random samples and statistical models
245(3)
17.2 Distribution features and sample statistics
248(5)
17.3 Estimating features of the "true" distribution
253(3)
17.4 The linear regression model
256(3)
17.5 Solutions to the quick exercises
259(1)
17.6 Exercises
259(10)
18 The bootstrap 269(16)
18.1 The bootstrap principle
269(3)
18.2 The empirical bootstrap
272(4)
18.3 The parametric bootstrap
276(3)
18.4 Solutions to the quick exercises
279(1)
18.5 Exercises
280(5)
19 Unbiased estimators 285(14)
19.1 Estimators
285(2)
19.2 Investigating the behavior of an estimator
287(1)
19.3 The sampling distribution and unbiasedness
288(4)
19.4 Unbiased estimators for expectation and variance
292(2)
19.5 Solutions to the quick exercises
294(1)
19.6 Exercises
294(5)
20 Efficiency and mean squared error 299(14)
20.1 Estimating the number of German tanks
299(3)
20.2 Variance of an estimator
302(3)
20.3 Mean squared error
305(2)
20.4 Solutions to the quick exercises
307(1)
20.5 Exercises
307(6)
21 Maximum likelihood 313(16)
21.1 Why a general principle?
313(1)
21.2 The maximum likelihood principle
314(2)
21.3 Likelihood and loglikelihood
316(5)
21.4 Properties of maximum likelihood estimators
321(1)
21.5 Solutions to the quick exercises
322(1)
21.6 Exercises
323(6)
22 The method of least squares 329(12)
22.1 Least squares estimation and regression
329(3)
22.2 Residuals
332(3)
22.3 Relation with maximum likelihood
335(1)
22.4 Solutions to the quick exercises
336(1)
22.5 Exercises
337(4)
23 Confidence intervals for the mean 341(20)
23.1 General principle
341(4)
23.2 Normal data
345(5)
23.3 Bootstrap confidence intervals
350(3)
23.4 Large samples
353(2)
23.5 Solutions to the quick exercises
355(1)
23.6 Exercises
356(5)
24 More on confidence intervals 361(12)
24.1 The probability of success
361(3)
24.2 Is there a general method?
364(2)
24.3 One-sided confidence intervals
366(1)
24.4 Determining the sample size
367(1)
24.5 Solutions to the quick exercises
368(1)
24.6 Exercises
369(4)
25 Testing hypotheses: essentials 373(10)
25.1 Null hypothesis and test statistic
373(3)
25.2 Tail probabilities
376(1)
25.3 Type I and type II errors
377(2)
25.4 Solutions to the quick exercises
379(1)
25.5 Exercises
380(3)
26 Testing hypotheses: elaboration 383(16)
26.1 Significance level
383(3)
26.2 Critical region and critical values
386(4)
26.3 Type II error
390(2)
26.4 Relation with confidence intervals
392(1)
26.5 Solutions to the quick exercises
393(1)
26.6 Exercises
394(5)
27 The t-test 399(16)
27.1 Monitoring the production of ball bearings
399(2)
27.2 The one-sample t-test
401(4)
27.3 The t-test in a regression setting
405(4)
27.4 Solutions to the quick exercises
409(1)
27.5 Exercises
410(5)
28 Comparing two samples 415(14)
28.1 Is dry drilling faster than wet drilling?
415(1)
28.2 Two samples with equal variances
416(3)
28.3 Two samples with unequal variances
419(3)
28.4 Large samples
422(2)
28.5 Solutions to the quick exercises
424(1)
28.6 Exercises
424(5)
A Summary of distributions 429(2)
B Tables of the normal and t-distributions 431(4)
C Answers to selected exercises 435(10)
D Full solutions to selected exercises 445(30)
References 475(2)
List of symbols 477(2)
Index 479


Michel Dekking, Cor Kraaikamp, Rik Lopuhaä and Ludolf Meester are professors in the Department of Applied Mathematics at TU Delft, The Netherlands. The material in this book has been successfully taught there for several years, and at the University of Leiden, The Netherlands, and Wesleyan University, USA, since 2003.
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