Modern Introduction to Probability and Statistics Understanding Why and How

ISBN-10: 1852338962
ISBN-13: 9781852338961
Edition: 2005
List price: $59.95 Buy it from $19.86 Rent it from $20.59
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Description: 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. The strength of this  More...

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Book details

List price: $59.95
Copyright year: 2005
Publisher: Springer
Publication date: 2/19/2007
Binding: Mixed Media
Pages: 488
Size: 6.50" wide x 9.50" long x 1.25" tall
Weight: 1.782
Language: English

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. The strength of this book is that it 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. A Modern Introduction to Probability and Statistics has numerous quick exercises to give direct feedback to students. In addition there are 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 pre-requisite 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 modern methods such as the bootstrap.

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.

Why probability and statistics?
Biometry: iris recognition
Killer football
Cars and goats: the Monty Hall dilemma
The space shuttle Challenger
Statistics versus intelligence agencies
The speed of light
Outcomes, events, and probability
Sample spaces
Events
Probability
Products of sample spaces
An infinite sample space
Solutions to the quick exercises
Exercises
Conditional probability and independence
Conditional probability
The multiplication rule
The law of total probability and Bayes' rule
Independence
Solutions to the quick exercises
Exercises
Discrete random variables
Random variables
The probability distribution of a discrete random variable
The Bernoulli and binomial distributions
The geometric distribution
Solutions to the quick exercises
Exercises
Continuous random variables
Probability density functions
The uniform distribution
The exponential distribution
The Pareto distribution
The normal distribution
Quantiles
Solutions to the quick exercises
Exercises
Simulation
What is simulation?
Generating realizations of random variables
Comparing two jury rules
The single-server queue
Solutions to the quick exercises
Exercises
Expectation and variance
Expected values
Three examples
The change-of-variable formula
Variance
Solutions to the quick exercises
Exercises
Computations with random variables
Transforming discrete random variables
Transforming continuous random variables
Jensen's inequality
Extremes
Solutions to the quick exercises
Exercises
Joint distributions and independence
Joint distributions of discrete random variables
Joint distributions of continuous random variables
More than two random variables
Independent random variables
Propagation of independence
Solutions to the quick exercises
Exercises
Covariance and correlation
Expectation and joint distributions
Covariance
The correlation coefficient
Solutions to the quick exercises
Exercises
More computations with more random variables
Sums of discrete random variables
Sums of continuous random variables
Product and quotient of two random variables
Solutions to the quick exercises
Exercises
The Poisson process
Random points
Taking a closer look at random arrivals
The one-dimensional Poisson process
Higher-dimensional Poisson processes
Solutions to the quick exercises
Exercises
The law of large numbers
Averages vary less
Chebyshev's inequality
The law of large numbers
Consequences of the law of large numbers
Solutions to the quick exercises
Exercises
The central limit theorem
Standardizing averages
Applications of the central limit theorem
Solutions to the quick exercises
Exercises
Exploratory data analysis: graphical summaries
Example: the Old Faithful data
Histograms
Kernel density estimates
The empirical distribution function
Scatterplot
Solutions to the quick exercises
Exercises
Exploratory data analysis: numerical summaries
The center of a dataset
The amount of variability of a dataset
Empirical quantiles, quartiles, and the IQR
The box-and-whisker plot
Solutions to the quick exercises
Exercises
Basic statistical models
Random samples and statistical models
Distribution features and sample statistics
Estimating features of the "true" distribution
The linear regression model
Solutions to the quick exercises
Exercises
The bootstrap
The bootstrap principle
The empirical bootstrap
The parametric bootstrap
Solutions to the quick exercises
Exercises
Unbiased estimators
Estimators
Investigating the behavior of an estimator
The sampling distribution and unbiasedness
Unbiased estimators for expectation and variance
Solutions to the quick exercises
Exercises
Efficiency and mean squared error
Estimating the number of German tanks
Variance of an estimator
Mean squared error
Solutions to the quick exercises
Exercises
Maximum likelihood
Why a general principle?
The maximum likelihood principle
Likelihood and loglikelihood
Properties of maximum likelihood estimators
Solutions to the quick exercises
Exercises
The method of least squares
Least squares estimation and regression
Residuals
Relation with maximum likelihood
Solutions to the quick exercises
Exercises
Confidence intervals for the mean
General principle
Normal data
Bootstrap confidence intervals
Large samples
Solutions to the quick exercises
Exercises
More on confidence intervals
The probability of success
Is there a general method?
One-sided confidence intervals
Determining the sample size
Solutions to the quick exercises
Exercises
Testing hypotheses: essentials
Null hypothesis and test statistic
Tail probabilities
Type I and type II errors
Solutions to the quick exercises
Exercises
Testing hypotheses: elaboration
Significance level
Critical region and critical values
Type II error
Relation with confidence intervals
Solutions to the quick exercises
Exercises
The t-test
Monitoring the production of ball bearings
The one-sample t-test
The t-test in a regression setting
Solutions to the quick exercises
Exercises
Comparing two samples
Is dry drilling faster than wet drilling?
Two samples with equal variances
Two samples with unequal variances
Large samples
Solutions to the quick exercises
Exercises
Summary of distributions
Tables of the normal and t-distributions
Answers to selected exercises
Full solutions to selected exercises
References
List of symbols
Index

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