Bridging the gap between statistical theory and physical experiment, this is a thorough introduction to the statistical methods used in the experimental physical sciences and to the numerical methods used to implement them. The treatment emphasises concise but rigorous mathematics but always retains its focus on applications. Readers are assumed to have a sound basic knowledge of differential and integral calculus and some knowledge of vectors and matrices. After an introduction to probability, random variables, computer generation of random numbers and important distributions, the book turns to statistical samples, the maximum likelihood method, and the testing of statistical hypotheses. The discussion concludes with several important statistical methods: least squares, analysis of variance, polynomial regression, and analysis of time series. Appendices provide the necessary methods of matrix algebra, combinatorics, and many sets of useful algorithms and formulae.

1 Introduction.- 1.1 Typical Problems of Data Analysis.- 1.2 On the Structure of this Book.- 1.3 About the Computer Programs.- 2 Probabilities.- 2.1 Experiments, Events, Sample Space.- 2.2 The Concept of Probability.- 2.3 Rules of Probability Calculus. Conditional Probability.- 2.4 Examples.- 2.4.1 Probability for n Dots in the Throwing of Two Dice.- 2.4.2 Lottery 6 out of 49.- 2.4.3 Three-Door Game.- 2.5 Problems.- 2.5.1 Determination of Probabilities through Symmetry Considerations.- 2.5.2 Probability for Non-exclusive Events.- 2.5.3 Dependent and Independent Events.- 2.5.4 Complementary Events.- 2.5.5 Probabilities Drawn from Large and Small Populations.- 2.6 Hints and Solutions.- 3 Random Variables. Distributions.- 3.1 Random Variables.- 3.2 Distributions of a Single Random Variable.- 3.3 Functions of a Single Random Variable, Expectation Value, Variance, Moments.- 3.4 Distribution Function and Probability Density of Two Variables. Conditional Probability.- 3.5 Expectation Values, Variance, Covariance, and Correlation.- 3.6 More than Two Variables. Vector and Matrix Notation.- 3.7 Transformation of Variables.- 3.8 Linear and Orthogonal Transformations. Error Propagation.- 3.9 Problems.- 3.9.1 Mean, Variance, and Skewness of a Discrete Distribution.- 3.9.2 Mean, Mode, Median, and Variance of a Continuous Distribution.- 3.9.3 Transformation of a Single Variable.- 3.9.4 Transformation of Several Variables.- 3.9.5 Error Propagation.- 3.9.6 Covariance and Correlation.- 3.10 Hints and Solutions.- 4 Computer Generated Random Numbers.The Monte Carlo Method.- 4.1 Random Numbers.- 4.2 Representation of Numbers in a Computer.- 4.3 Linear Congruential Generators.- 4.4 Multiplicative Linear Congruential Generators.- 4.5 Quality of an MLCG. Spectral Test.- 4.6 Implementation and Portability of an MLCG.- 4.7 Combination of Several MLCGs.- 4.8 Program for Generation of Uniformly Distributed Random Numbers.- 4.9 Generation of Arbitrarily Distributed Random Numbers.- 4.9.1 Generation by Transformation of the Uniform Distribution.- 4.9.2 Generation with the von Neumann Acceptance-Rejection Technique.- 4.10 Generation of Normally Distributed Random Numbers.- 4.11 Generation of Random Numbers According to a Multivariate Normal Distribution.- 4.12 The Monte Carlo Method for Integration.- 4.13 The Monte Carlo Method for Simulation.- 4.14 Example Programs.- 4.14.1 Main Program E1RN to Demonstrate Subprograms RNMLCG, RNECUY, and RNSTNR.- 4.14.2 Main Program E2RN to Demonstrate Subprogram RNLINE.- 4.14.3 Main Program E3RN to Demonstrate Subprogram RNRADI.- 4.14.4 Main Program E4RN to Simulate Molecular Movement of a Gas.- 4.14.5 Main Program E5RN to Demonstrate Subprograms RNMNPR and RNMNGN.- 4.15 Programming Problems.- 4.15.1 Program to Generate Breit-Wigner-Distributed Random Numbers.- 4.15.2 Program to Generate Random Numbers from a Triangular Distribution.- 4.15.3 Program to Generate Data Points with Errors of Different Size.- 4.15.4 Programs to Simulate Molecular Movement.- 5 Some Important Distributions and Theorems.- 5.1 The Binomial and Multinomial Distributions.- 5.2 Frequency. The Law of Large Numbers.- 5.3 The Hypergeometric Distribution.- 5.4 The Poisson Distribution.- 5.5 The Characteristic Function of a Distribution.- 5.6 The Standard Normal Distribution.- 5.7 The Normal or Gaussian Distribution.- 5.8 Quantitative Properties of the Normal Distribution.- 5.9 The Central Limit Theorem.- 5.10 The Multivariate Normal Distribution.- 5.11 Convolutions of Distributions.- 5.11.1 Folding Integrals.- 5.11.2 Convolutions with the Normal Distribution.- 5.12 Example Programs.- 5.12.1 Main Program E1DS to Simulate Empirical Frequency and Demonstrate Statistical Fluctuations.- 5.12.2 Main Program E2DS to Simulate the Experiment of Rutherford and Geiger.- 5.12.3 Main Program E3DS to Simulate Galton's Board.- 5.13 Problems.- 5.13.1 Binomial Distribution.- 5.13.2 Poisson Distribution.- 5.13.3 Normal Distribution.- 5.13.4 Multivariate Normal Distribution.- 5.13.5 Convolution.- 5.14 Programming Problems.- 5.14.1 Convolution of Uniform Distributions.- 5.14.2 Convolution of Uniform Distribution and Normal Distribution.- 5.15 Hints and Solutions.- 6 Samples.- 6.1 Random Samples. Distribution of a Sample. Estimators.- 6.2 Samples from Continuous Populations. Mean and Variance of a Sample.- 6.3 Graphical Representation of Samples. Histograms and Scatter Plots.- 6.4 Samples from Partitioned Populations.- 6.5 Samples without Replacement from Finite Discrete Populations. Mean Square Deviation. Degrees of Freedom.- 6.6 Samples from Gaussian Distributions. ?2-Distribution.- 6.7 ?2 and Empirical Variance.- 6.8 Sampling by Counting. Small Samples.- 6.9 Small Samples with Background.- 6.10 Determining a Ratio of Small Numbers of Events.- 6.11 Ratio of Small Numbers of Events with Background.- 6.12 Example Programs.- 6.12.1 Main Program E1 SM to Demonstrate Subprogram SMMNVR.- 6.12.2 Main Program E2 SM to Demonstrate Subprograms SMHSIN, SMHSFL, and SMHSGR.- 6.12.3 Main Program E3 SM to Demonstrate Subprogram SMSDGR.- 6.12.4 Main Program E4 SM to Demonstrate Subprogram SMERSS.- 6.12.5 Main Program E5 SM to Demonstrate Subprogram SMERQS.- 6.12.6 Main Program E6 SM to Simulate Experiments with Few Events and Background.- 6.12.7 Main Program E7 SM to Simulate Experiments with Few Signal Events and with Reference Events.- 6.13 Problems.- 6.13.1 Efficiency of Estimators.- 6.13.2 Sample Mean and Sample Variance.- 6.13.3 Samples from a Partitioned Population.- 6.13.4 ?2-distribution.- 6.13.5 Histogram.- 6.14 Hints and Solutions.- 7 The Method of Maximum Likelihood.- 7.1 Likelihood Ratio. Likelihood Function.- 7.2 The Method of Maximum Likelihood.- 7.3 Information Inequality. Minimum Variance Estimators. Sufficient Estimators.- 7.4 Asymptotic Properties of the Likelihood Function and Maximum-Likelihood Estimators.- 7.5 Simultaneous Estimation of Several Parameters. Confidence Intervals.- 7.6 Example Programs.- 7.6.1 Program E1ML to Compute the Mean Lifetime and Asymmetric Errors from a Small Number of Radioactive Decays.- 7.6.2 Program E2ML to Compute the Maximum-Likelihood Estimates of the Parameters of a Bivariate Normal Distribution from a Simulated Sample.- 7.7 Programming Problems.- 7.7.1 Distribution of Lifetimes Determined from a Small Number of Radioactive Decays.- 7.7.2 Distribution of the Sample Correlation Coefficient.- 7.8 Problems.- 7.8.1 Maximum-Likelihood Estimates.- 7.8.2 Information.- 7.8.3 Variance of an Estimator.- 7.9 Hints and Solutions.- 8 Testing Statistical Hypotheses.- 8.1 Introduction.- 8.2 F-Test on Equality of Variances.- 8.3 Student's Test. Comparison of Means.- 8.4 Concepts of the General Theory of Tests.- 8.5 The Neyman-Pearson Lemma and Applications.- 8.6 The Likelihood-Ratio Method.- 8.7 The ?2;-Test for Goodness-of-Fit.- 8.7.1 ?2;-test with Maximal Number of Degrees of Freedom.- 8.7.2 ?2;-test with Reduced Number of Degrees of Freedom.- 8.7.3 ?2;-Test and Empirical …