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A modern introduction to probability and statistics : understanding why and how / F.M. Dekking ... [et al.].

Contributor(s): Material type: TextTextSeries: Springer texts in statisticsPublication details: London : Springer, c2005.Description: xv, 486 p. : ill. ; 25 cmISBN:
  • 1852338962 (acid-free paper)
Subject(s): DDC classification:
  • 519.2   22
Contents:
Why probability and statistics?p. 1 Biometry: iris recognitionp. 1 Killer footballp. 3 Cars and goats: the Monty Hall dilemmap. 4 The space shuttle Challengerp. 5 Statistics versus intelligence agenciesp. 7 The speed of lightp. 9 Outcomes, events, and probabilityp. 13 Sample spacesp. 13 Eventsp. 14 Probabilityp. 16 Products of sample spacesp. 18 An infinite sample spacep. 19 Solutions to the quick exercisesp. 21 Exercisesp. 21 Conditional probability and independencep. 25 Conditional probabilityp. 25 The multiplication rulep. 27 The law of total probability and Bayes' rulep. 30 Independencep. 32 Solutions to the quick exercisesp. 35 Exercisesp. 37 Discrete random variablesp. 41 Random variablesp. 41 The probability distribution of a discrete random variablep. 43 The Bernoulli and binomial distributionsp. 45 The geometric distributionp. 48 Solutions to the quick exercisesp. 50 Exercisesp. 51 Continuous random variablesp. 57 Probability density functionsp. 57 The uniform distributionp. 60 The exponential distributionp. 61 The Pareto distributionp. 63 The normal distributionp. 64 Quantilesp. 65 Solutions to the quick exercisesp. 67 Exercisesp. 68 Simulationp. 71 What is simulation?p. 71 Generating realizations of random variablesp. 72 Comparing two jury rulesp. 75 The single-server queuep. 80 Solutions to the quick exercisesp. 84 Exercisesp. 85 Expectation and variancep. 89 Expected valuesp. 89 Three examplesp. 93 The change-of-variable formulap. 94 Variancep. 96 Solutions to the quick exercisesp. 99 Exercisesp. 99 Computations with random variablesp. 103 Transforming discrete random variablesp. 103 Transforming continuous random variablesp. 104 Jensen's inequalityp. 106 Extremesp. 108 Solutions to the quick exercisesp. 110 Exercisesp. 111 Joint distributions and independencep. 115 Joint distributions of discrete random variablesp. 115 Joint distributions of continuous random variablesp. 118 More than two random variablesp. 122 Independent random variablesp. 124 Propagation of independencep. 125 Solutions to the quick exercisesp. 126 Exercisesp. 127 Covariance and correlationp. 135 Expectation and joint distributionsp. 135 Covariancep. 138 The correlation coefficientp. 141 Solutions to the quick exercisesp. 143 Exercisesp. 144 More computations with more random variablesp. 151 Sums of discrete random variablesp. 151 Sums of continuous random variablesp. 154 Product and quotient of two random variablesp. 159 Solutions to the quick exercisesp. 162 Exercisesp. 163 The Poisson processp. 167 Random pointsp. 167 Taking a closer look at random arrivalsp. 168 The one-dimensional Poisson processp. 171 Higher-dimensional Poisson processesp. 173 Solutions to the quick exercisesp. 176 Exercisesp. 176 The law of large numbersp. 181 Averages vary lessp. 181 Chebyshev's inequalityp. 183 The law of large numbersp. 185 Consequences of the law of large numbersp. 188 Solutions to the quick exercisesp. 191 Exercisesp. 191 The central limit theoremp. 195 Standardizing averagesp. 195 Applications of the central limit theoremp. 199 Solutions to the quick exercisesp. 202 Exercisesp. 203 Exploratory data analysis: graphical summariesp. 207 Example: the Old Faithful datap. 207 Histogramsp. 209 Kernel density estimatesp. 212 The empirical distribution functionp. 219 Scatterplotp. 221 Solutions to the quick exercisesp. 225 Exercisesp. 226 Exploratory data analysis: numerical summariesp. 231 The center of a datasetp. 231 The amount of variability of a datasetp. 233 Empirical quantiles, quartiles, and the IQRp. 234 The box-and-whisker plotp. 236 Solutions to the quick exercisesp. 238 Exercisesp. 240 Basic statistical modelsp. 245 Random samples and statistical modelsp. 245 Distribution features and sample statisticsp. 248 Estimating features of the "true" distributionp. 253 The linear regression modelp. 256 Solutions to the quick exercisesp. 259 Exercisesp. 259 The bootstrapp. 269 The bootstrap principlep. 269 The empirical bootstrapp. 272 The parametric bootstrapp. 276 Solutions to the quick exercisesp. 279 Exercisesp. 280 Unbiased estimatorsp. 285 Estimatorsp. 285 Investigating the behavior of an estimatorp. 287 The sampling distribution and unbiasednessp. 288 Unbiased estimators for expectation and variancep. 292 Solutions to the quick exercisesp. 294 Exercisesp. 294 Efficiency and mean squared errorp. 299 Estimating the number of German tanksp. 299 Variance of an estimatorp. 302 Mean squared errorp. 305 Solutions to the quick exercisesp. 307 Exercisesp. 307 Maximum likelihoodp. 313 Why a general principle?p. 313 The maximum likelihood principlep. 314 Likelihood and loglikelihoodp. 316 Properties of maximum likelihood estimatorsp. 321 Solutions to the quick exercisesp. 322 Exercisesp. 323 The method of least squaresp. 329 Least squares estimation and regressionp. 329 Residualsp. 332 Relation with maximum likelihoodp. 335 Solutions to the quick exercisesp. 336 Exercisesp. 337 Confidence intervals for the meanp. 341 General principlep. 341 Normal datap. 345 Bootstrap confidence intervalsp. 350 Large samplesp. 353 Solutions to the quick exercisesp. 355 Exercisesp. 356 More on confidence intervalsp. 361 The probability of successp. 361 Is there a general method?p. 364 One-sided confidence intervalsp. 366 Determining the sample sizep. 367 Solutions to the quick exercisesp. 368 Exercisesp. 369 Testing hypotheses: essentialsp. 373 Null hypothesis and test statisticp. 373 Tail probabilitiesp. 376 Type I and type II errorsp. 377 Solutions to the quick exercisesp. 379 Exercisesp. 380 Testing hypotheses: elaborationp. 383 Significance levelp. 383 Critical region and critical valuesp. 386 Type II errorp. 390 Relation with confidence intervalsp. 392 Solutions to the quick exercisesp. 393 Exercisesp. 394 The t-testp. 399 Monitoring the production of ball bearingsp. 399 The one-sample t-testp. 401 The t-test in a regression settingp. 405 Solutions to the quick exercisesp. 409 Exercisesp. 410 Comparing two samplesp. 415 Is dry drilling faster than wet drilling?p. 415 Two samples with equal variancesp. 416 Two samples with unequal variancesp. 419 Large samplesp. 422 Solutions to the quick exercisesp. 424 Exercisesp. 424 Summary of distributionsp. 429 Tables of the normal and t-distributionsp. 431 Answers to selected exercisesp. 435 Full solutions to selected exercisesp. 445 Referencesp. 475 List of symbolsp. 477 Indexp. 479
Summary: 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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Item type Current library Call number Copy number Status Date due Barcode
Books Books Main library General Stacks 519.2 / DE.M 2005 (Browse shelf(Opens below)) 1 Available 003949

Includes bibliographical references (p. [475]-476) and index.

Why probability and statistics?p. 1 Biometry: iris recognitionp. 1 Killer footballp. 3 Cars and goats: the Monty Hall dilemmap. 4 The space shuttle Challengerp. 5 Statistics versus intelligence agenciesp. 7 The speed of lightp. 9 Outcomes, events, and probabilityp. 13 Sample spacesp. 13 Eventsp. 14 Probabilityp. 16 Products of sample spacesp. 18 An infinite sample spacep. 19 Solutions to the quick exercisesp. 21 Exercisesp. 21 Conditional probability and independencep. 25 Conditional probabilityp. 25 The multiplication rulep. 27 The law of total probability and Bayes' rulep. 30 Independencep. 32 Solutions to the quick exercisesp. 35 Exercisesp. 37 Discrete random variablesp. 41 Random variablesp. 41 The probability distribution of a discrete random variablep. 43 The Bernoulli and binomial distributionsp. 45 The geometric distributionp. 48 Solutions to the quick exercisesp. 50 Exercisesp. 51 Continuous random variablesp. 57 Probability density functionsp. 57 The uniform distributionp. 60 The exponential distributionp. 61 The Pareto distributionp. 63 The normal distributionp. 64 Quantilesp. 65 Solutions to the quick exercisesp. 67 Exercisesp. 68 Simulationp. 71 What is simulation?p. 71 Generating realizations of random variablesp. 72 Comparing two jury rulesp. 75 The single-server queuep. 80 Solutions to the quick exercisesp. 84 Exercisesp. 85 Expectation and variancep. 89 Expected valuesp. 89 Three examplesp. 93 The change-of-variable formulap. 94 Variancep. 96 Solutions to the quick exercisesp. 99 Exercisesp. 99 Computations with random variablesp. 103 Transforming discrete random variablesp. 103 Transforming continuous random variablesp. 104 Jensen's inequalityp. 106 Extremesp. 108 Solutions to the quick exercisesp. 110 Exercisesp. 111 Joint distributions and independencep. 115 Joint distributions of discrete random variablesp. 115 Joint distributions of continuous random variablesp. 118 More than two random variablesp. 122 Independent random variablesp. 124 Propagation of independencep. 125 Solutions to the quick exercisesp. 126 Exercisesp. 127 Covariance and correlationp. 135 Expectation and joint distributionsp. 135 Covariancep. 138 The correlation coefficientp. 141 Solutions to the quick exercisesp. 143 Exercisesp. 144 More computations with more random variablesp. 151 Sums of discrete random variablesp. 151 Sums of continuous random variablesp. 154 Product and quotient of two random variablesp. 159 Solutions to the quick exercisesp. 162 Exercisesp. 163 The Poisson processp. 167 Random pointsp. 167 Taking a closer look at random arrivalsp. 168 The one-dimensional Poisson processp. 171 Higher-dimensional Poisson processesp. 173 Solutions to the quick exercisesp. 176 Exercisesp. 176 The law of large numbersp. 181 Averages vary lessp. 181 Chebyshev's inequalityp. 183 The law of large numbersp. 185 Consequences of the law of large numbersp. 188 Solutions to the quick exercisesp. 191 Exercisesp. 191 The central limit theoremp. 195 Standardizing averagesp. 195 Applications of the central limit theoremp. 199 Solutions to the quick exercisesp. 202 Exercisesp. 203 Exploratory data analysis: graphical summariesp. 207 Example: the Old Faithful datap. 207 Histogramsp. 209 Kernel density estimatesp. 212 The empirical distribution functionp. 219 Scatterplotp. 221 Solutions to the quick exercisesp. 225 Exercisesp. 226 Exploratory data analysis: numerical summariesp. 231 The center of a datasetp. 231 The amount of variability of a datasetp. 233 Empirical quantiles, quartiles, and the IQRp. 234 The box-and-whisker plotp. 236 Solutions to the quick exercisesp. 238 Exercisesp. 240 Basic statistical modelsp. 245 Random samples and statistical modelsp. 245 Distribution features and sample statisticsp. 248 Estimating features of the "true" distributionp. 253 The linear regression modelp. 256 Solutions to the quick exercisesp. 259 Exercisesp. 259 The bootstrapp. 269 The bootstrap principlep. 269 The empirical bootstrapp. 272 The parametric bootstrapp. 276 Solutions to the quick exercisesp. 279 Exercisesp. 280 Unbiased estimatorsp. 285 Estimatorsp. 285 Investigating the behavior of an estimatorp. 287 The sampling distribution and unbiasednessp. 288 Unbiased estimators for expectation and variancep. 292 Solutions to the quick exercisesp. 294 Exercisesp. 294 Efficiency and mean squared errorp. 299 Estimating the number of German tanksp. 299 Variance of an estimatorp. 302 Mean squared errorp. 305 Solutions to the quick exercisesp. 307 Exercisesp. 307 Maximum likelihoodp. 313 Why a general principle?p. 313 The maximum likelihood principlep. 314 Likelihood and loglikelihoodp. 316 Properties of maximum likelihood estimatorsp. 321 Solutions to the quick exercisesp. 322 Exercisesp. 323 The method of least squaresp. 329 Least squares estimation and regressionp. 329 Residualsp. 332 Relation with maximum likelihoodp. 335 Solutions to the quick exercisesp. 336 Exercisesp. 337 Confidence intervals for the meanp. 341 General principlep. 341 Normal datap. 345 Bootstrap confidence intervalsp. 350 Large samplesp. 353 Solutions to the quick exercisesp. 355 Exercisesp. 356 More on confidence intervalsp. 361 The probability of successp. 361 Is there a general method?p. 364 One-sided confidence intervalsp. 366 Determining the sample sizep. 367 Solutions to the quick exercisesp. 368 Exercisesp. 369 Testing hypotheses: essentialsp. 373 Null hypothesis and test statisticp. 373 Tail probabilitiesp. 376 Type I and type II errorsp. 377 Solutions to the quick exercisesp. 379 Exercisesp. 380 Testing hypotheses: elaborationp. 383 Significance levelp. 383 Critical region and critical valuesp. 386 Type II errorp. 390 Relation with confidence intervalsp. 392 Solutions to the quick exercisesp. 393 Exercisesp. 394 The t-testp. 399 Monitoring the production of ball bearingsp. 399 The one-sample t-testp. 401 The t-test in a regression settingp. 405 Solutions to the quick exercisesp. 409 Exercisesp. 410 Comparing two samplesp. 415 Is dry drilling faster than wet drilling?p. 415 Two samples with equal variancesp. 416 Two samples with unequal variancesp. 419 Large samplesp. 422 Solutions to the quick exercisesp. 424 Exercisesp. 424 Summary of distributionsp. 429 Tables of the normal and t-distributionsp. 431 Answers to selected exercisesp. 435 Full solutions to selected exercisesp. 445 Referencesp. 475 List of symbolsp. 477 Indexp. 479

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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