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A Modern Introduction to Probability and Statistics
Understanding Why and How
By: F.M. Dekking, C. Kraaikamp, H.P. Lopuhaae, L.E. Meester
Hardcover | 15 June 2005 | Edition Number 1
At a Glance
488 Pages
23.5 x 15.5 x 2.69
Hardcover
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Industry Reviews
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)
Why probability and statistics? | p. 1 |
Biometry: iris recognition | p. 1 |
Killer football | p. 3 |
Cars and goats: the Monty Hall dilemma | p. 4 |
The space shuttle Challenger | p. 5 |
Statistics versus intelligence agencies | p. 7 |
The speed of light | p. 9 |
Outcomes, events, and probability | p. 13 |
Sample spaces | p. 13 |
Events | p. 14 |
Probability | p. 16 |
Products of sample spaces | p. 18 |
An infinite sample space | p. 19 |
Solutions to the quick exercises | p. 21 |
Exercises | p. 21 |
Conditional probability and independence | p. 25 |
Conditional probability | p. 25 |
The multiplication rule | p. 27 |
The law of total probability and Bayes' rule | p. 30 |
Independence | p. 32 |
Solutions to the quick exercises | p. 35 |
Exercises | p. 37 |
Discrete random variables | p. 41 |
Random variables | p. 41 |
The probability distribution of a discrete random variable | p. 43 |
The Bernoulli and binomial distributions | p. 45 |
The geometric distribution | p. 48 |
Solutions to the quick exercises | p. 50 |
Exercises | p. 51 |
Continuous random variables | p. 57 |
Probability density functions | p. 57 |
The uniform distribution | p. 60 |
The exponential distribution | p. 61 |
The Pareto distribution | p. 63 |
The normal distribution | p. 64 |
Quantiles | p. 65 |
Solutions to the quick exercises | p. 67 |
Exercises | p. 68 |
Simulation | p. 71 |
What is simulation? | p. 71 |
Generating realizations of random variables | p. 72 |
Comparing two jury rules | p. 75 |
The single-server queue | p. 80 |
Solutions to the quick exercises | p. 84 |
Exercises | p. 85 |
Expectation and variance | p. 89 |
Expected values | p. 89 |
Three examples | p. 93 |
The change-of-variable formula | p. 94 |
Variance | p. 96 |
Solutions to the quick exercises | p. 99 |
Exercises | p. 99 |
Computations with random variables | p. 103 |
Transforming discrete random variables | p. 103 |
Transforming continuous random variables | p. 104 |
Jensen's inequality | p. 106 |
Extremes | p. 108 |
Solutions to the quick exercises | p. 110 |
Exercises | p. 111 |
Joint distributions and independence | p. 115 |
Joint distributions of discrete random variables | p. 115 |
Joint distributions of continuous random variables | p. 118 |
More than two random variables | p. 122 |
Independent random variables | p. 124 |
Propagation of independence | p. 125 |
Solutions to the quick exercises | p. 126 |
Exercises | p. 127 |
Covariance and correlation | p. 135 |
Expectation and joint distributions | p. 135 |
Covariance | p. 138 |
The correlation coefficient | p. 141 |
Solutions to the quick exercises | p. 143 |
Exercises | p. 144 |
More computations with more random variables | p. 151 |
Sums of discrete random variables | p. 151 |
Sums of continuous random variables | p. 154 |
Product and quotient of two random variables | p. 159 |
Solutions to the quick exercises | p. 162 |
Exercises | p. 163 |
The Poisson process | p. 167 |
Random points | p. 167 |
Taking a closer look at random arrivals | p. 168 |
The one-dimensional Poisson process | p. 171 |
Higher-dimensional Poisson processes | p. 173 |
Solutions to the quick exercises | p. 176 |
Exercises | p. 176 |
The law of large numbers | p. 181 |
Averages vary less | p. 181 |
Chebyshev's inequality | p. 183 |
The law of large numbers | p. 185 |
Consequences of the law of large numbers | p. 188 |
Solutions to the quick exercises | p. 191 |
Exercises | p. 191 |
The central limit theorem | p. 195 |
Standardizing averages | p. 195 |
Applications of the central limit theorem | p. 199 |
Solutions to the quick exercises | p. 202 |
Exercises | p. 203 |
Exploratory data analysis: graphical summaries | p. 207 |
Example: the Old Faithful data | p. 207 |
Histograms | p. 209 |
Kernel density estimates | p. 212 |
The empirical distribution function | p. 219 |
Scatterplot | p. 221 |
Solutions to the quick exercises | p. 225 |
Exercises | p. 226 |
Exploratory data analysis: numerical summaries | p. 231 |
The center of a dataset | p. 231 |
The amount of variability of a dataset | p. 233 |
Empirical quantiles, quartiles, and the IQR | p. 234 |
The box-and-whisker plot | p. 236 |
Solutions to the quick exercises | p. 238 |
Exercises | p. 240 |
Basic statistical models | p. 245 |
Random samples and statistical models | p. 245 |
Distribution features and sample statistics | p. 248 |
Estimating features of the "true" distribution | p. 253 |
The linear regression model | p. 256 |
Solutions to the quick exercises | p. 259 |
Exercises | p. 259 |
The bootstrap | p. 269 |
The bootstrap principle | p. 269 |
The empirical bootstrap | p. 272 |
The parametric bootstrap | p. 276 |
Solutions to the quick exercises | p. 279 |
Exercises | p. 280 |
Unbiased estimators | p. 285 |
Estimators | p. 285 |
Investigating the behavior of an estimator | p. 287 |
The sampling distribution and unbiasedness | p. 288 |
Unbiased estimators for expectation and variance | p. 292 |
Solutions to the quick exercises | p. 294 |
Exercises | p. 294 |
Efficiency and mean squared error | p. 299 |
Estimating the number of German tanks | p. 299 |
Variance of an estimator | p. 302 |
Mean squared error | p. 305 |
Solutions to the quick exercises | p. 307 |
Exercises | p. 307 |
Maximum likelihood | p. 313 |
Why a general principle? | p. 313 |
The maximum likelihood principle | p. 314 |
Likelihood and loglikelihood | p. 316 |
Properties of maximum likelihood estimators | p. 321 |
Solutions to the quick exercises | p. 322 |
Exercises | p. 323 |
The method of least squares | p. 329 |
Least squares estimation and regression | p. 329 |
Residuals | p. 332 |
Relation with maximum likelihood | p. 335 |
Solutions to the quick exercises | p. 336 |
Exercises | p. 337 |
Confidence intervals for the mean | p. 341 |
General principle | p. 341 |
Normal data | p. 345 |
Bootstrap confidence intervals | p. 350 |
Large samples | p. 353 |
Solutions to the quick exercises | p. 355 |
Exercises | p. 356 |
More on confidence intervals | p. 361 |
The probability of success | p. 361 |
Is there a general method? | p. 364 |
One-sided confidence intervals | p. 366 |
Determining the sample size | p. 367 |
Solutions to the quick exercises | p. 368 |
Exercises | p. 369 |
Testing hypotheses: essentials | p. 373 |
Null hypothesis and test statistic | p. 373 |
Tail probabilities | p. 376 |
Type I and type II errors | p. 377 |
Solutions to the quick exercises | p. 379 |
Exercises | p. 380 |
Testing hypotheses: elaboration | p. 383 |
Significance level | p. 383 |
Critical region and critical values | p. 386 |
Type II error | p. 390 |
Relation with confidence intervals | p. 392 |
Solutions to the quick exercises | p. 393 |
Exercises | p. 394 |
The t-test | p. 399 |
Monitoring the production of ball bearings | p. 399 |
The one-sample t-test | p. 401 |
The t-test in a regression setting | p. 405 |
Solutions to the quick exercises | p. 409 |
Exercises | p. 410 |
Comparing two samples | p. 415 |
Is dry drilling faster than wet drilling? | p. 415 |
Two samples with equal variances | p. 416 |
Two samples with unequal variances | p. 419 |
Large samples | p. 422 |
Solutions to the quick exercises | p. 424 |
Exercises | p. 424 |
Summary of distributions | p. 429 |
Tables of the normal and t-distributions | p. 431 |
Answers to selected exercises | p. 435 |
Full solutions to selected exercises | p. 445 |
References | p. 475 |
List of symbols | p. 477 |
Index | p. 479 |
Table of Contents provided by Ingram. All Rights Reserved. |
ISBN: 9781852338961
ISBN-10: 1852338962
Series: Springer Texts in Statistics
Published: 15th June 2005
Format: Hardcover
Language: English
Number of Pages: 488
Audience: Professional and Scholarly
Publisher: Springer London Ltd
Country of Publication: GB
Edition Number: 1
Dimensions (cm): 23.5 x 15.5 x 2.69
Weight (kg): 0.86
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