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roe b probability statistics experimental physics 2001

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Textbook in PDF and DJVU formats Preface Basic Probability Concepts Some Initial Definitions Worked Problems Exercises Some Results Independent of Specific Distributions Multiple Scattering and the Root N Law Propagation of Errors; Errors When Changing Variables Some Useful Inequalities Worked Problems Exercises Discrete Distributions and Combinatorials Worked Problems Exercises Specific Discrete Distributions Binomial Distribution Poisson Distribution Worked Problems Exercises The Normal (or Gaussian) Distribution and Other Continuous Distributions The Normal Distribution The Chi-square Distribution F Distribution Student's Distribution The Uniform Distribution The Log-Normal Distribution The Cauchy Distribution (Breit-Wigner Distribution) Worked Problems Exercises Generating Functions and Characteristic Functions Introduction Convolutions and Compound Probability Generating Functions Characteristic Functions Exercises The Monte Carlo Method: Computer Simulation of Experiments Using the Distribution Inverse Method of Composition Acceptance Rejection Method Computer Pseudorandom Number Generators Unusual Application of a Pseudorandom Number String Worked Problems Exercises Queueing Theory and Other Probability Questions Queueing Theory Markov Chains Games of Chance Gambler's Ruin Exercises Two-Dimensional and Multidimensional Distributions Introduction Two-Dimensional Distributions Multidimensional Distributions Theorems on Sums of Squares Exercises The Central Limit Theorem Introduction; Lindeberg Criterion Failures of the Central Limit Theorem Khintchine's Law of the Iterated Logarithm Worked Problems Exercises Inverse Probability; Confidence Limits Bayes' Theorem The Problem of A Priori Probability Confidence Intervals and Their Interpretation Use of Confidence Intervals for Discrete Distributions Improving on the Symmetric Tails Confidence Limits When Is a Signal Significant? Worked Problems Exercises Methods for Estimating Parameters Least Squares and Maximum Likelihood Method of Least Squares (Regression Analysis) Maximum Likelihood Method Further Considerations in Fitting Histograms Improvement over Symmetric Tails Confidence Limits for Events With Partial Background-Signal Separation Estimation of a Correlation Coefficient Putting Together Several Probability Estimates Worked Problems Exercises Curve Fitting The Maximum Likelihood Method for Multiparameter Problems Regression Analysis with Non-constant Variance The Gibbs' Phenomenon The Regularization Method Other Regularization Schemes Fitting Data With Errors in Both x and y Non-linear Parameters Optimizing a Data Set With Signal and Background Robustness of Estimates Worked Problems Exercises Bartlett S Fonction; Estimating Likelihood Ratios Needed for an Experiment Introduction The Jacknife Making the Distribution Function of the Estimate Close to Normal; the Bartlett S Function Likelihood Ratio Estimating in Advance the Number of Events Needed for an Experiment Exercises Interpolating Functions and Unfolding Problems Interpolating Functions Spline Functions B-Splines Unfolding Data Exercises Fitting Data with Correlations and Constraints Introduction General Equations for Minimization Iterations and Correlation Matrices Beyond Maximum Likelihood and Least Squares; Robust Methods Introduction Tests on the Distribution Function Tests Based on the Binomial Distribution Tests Based on the Distributions of Deviations in Individual Bins of a Histogram Exercises References Index

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Roe B. Probability and Statistics in Experimental Physics 2001.djvu 3.1 MB
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roe b probability statistics experimental physics 2001

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