| Basic Characteristics of Error Distribution; Histograms | p. 1 |
| Introductory Remarks; Histograms | p. 1 |
| The Average of a Sample of Measurements | p. 3 |
| Dispersion Measures in Error Analysis | p. 4 |
| Cumulative Frequency Distribution | p. 6 |
| Examples of Empirical Distributions | p. 7 |
| Parameters Obtained from the Measured Data and Their Theoretical Values | p. 9 |
| References | p. 13 |
| Random Variables and Probability; Normal Distribution | p. 15 |
| Probability and Random Variables | p. 15 |
| The Cumulative Distribution Function; the Probability Density Function | p. 20 |
| Moments | p. 23 |
| The Normal Probability Distribution | p. 26 |
| Two-dimensional Gravity Flow of Granular Material | p. 38 |
| References | p. 47 |
| Probability Distributions and Their Characterizations | p. 49 |
| The Characteristic Function of a Distribution | p. 49 |
| Constants Characterizing the Random Variables | p. 51 |
| Deterministic Functions of Random Variables | p. 56 |
| Some Other One-dimensional Distributions | p. 57 |
| Discrete Probability Distributions | p. 57 |
| Continuous Probability Distributions | p. 60 |
| Remarks on Other Probability Distributions | p. 75 |
| Measures of Deviation from the Normal Distribution | p. 77 |
| Approximate Methods for Constructing a Probability Density Function | p. 79 |
| Multi-dimensional Probability Distributions | p. 81 |
| References | p. 89 |
| Functions of Independent Random Variables | p. 91 |
| Basic Relations | p. 91 |
| Simple Examples of Applications | p. 95 |
| Examples of Applications in Non-direct Measurements | p. 96 |
| Remarks on Applications in the Calculus of Tolerance Limits | p. 98 |
| Statical Analogy in the Analysis of Complex Dimension Nets | p. 100 |
| References | p. 105 |
| Two-dimensional Distributions | p. 107 |
| Introductory remarks | p. 107 |
| Linear Regression of Experimental Observations | p. 112 |
| Nonparametric Regression | p. 114 |
| The Method of Least Squares for Determining the Linear Regression Line | p. 116 |
| The Method of Moments for Determining the Linear Regression Line | p. 118 |
| Linear Correlation Between Experimentally Determined Quantities | p. 121 |
| Two-dimenstional Continuous Random Variables | p. 125 |
| The Two-dimensional Normal Distribution | p. 128 |
| The Case of Independent Random Variables | p. 128 |
| The Circular Normal Distribution | p. 130 |
| Three-dimensional Gravity Flow of Granular Media | p. 133 |
| The Case of Dependent Random Variables | p. 140 |
| References | p. 146 |
| Two-dimensional Functions of Independent Random Variables | p. 149 |
| Basic Relations | p. 149 |
| The Rectangular Distribution of Independent Random Variables | p. 153 |
| Analytical Method for Determining Two-dimensional Tolerance Limits Polygons | p. 153 |
| Statical Analogy Method for Determining Two-dimensional Tolerance Limit Polygons | p. 157 |
| Graphical Method for Determining Two-dimensional Tolerance Limit Polygon. Williot's Diagram | p. 161 |
| The Normal Distribution of Independent Random Variables | p. 165 |
| Indirect Determination of the Ellipses of Probability Concentration | p. 169 |
| References | p. 173 |
| Three-dimensional Distributions | p. 175 |
| General Remarks | p. 175 |
| Continuous Three-dimensional Random Variables | p. 177 |
| The Three-dimensional Normal Distribution | p. 180 |
| Independent Random Variables | p. 180 |
| The Spherical Normal Distribution | p. 181 |
| The Case of Dependent Random Variables | p. 183 |
| References | p. 186 |
| Three-dimensional Functions of Independent Random Variables | p. 189 |
| Basic Relations | p. 189 |
| The Rectangular Distribution of Independent Random Variables | p. 193 |
| The Normal Distribution of Independent Random Variables | p. 201 |
| Indirect Determination of the Ellipsoids of Probability Concentration | p. 205 |
| References | p. 209 |
| Problems Described by Implicit Equations | p. 211 |
| Introduction | p. 211 |
| Statistically Independent Random Variables | p. 213 |
| Two Independent Random Variables | p. 213 |
| A Function of Independent Random Variables | p. 215 |
| Statistically Dependent Random Variables | p. 219 |
| Two Dependent Random Variables | p. 219 |
| The Case of Gaussian Random Variables | p. 221 |
| More Random Variables: the Rosenblatt Transformation | p. 224 |
| Computational Problems | p. 227 |
| References | p. 230 |
| Useful Definitions and Facts of Probability Theory for Further Reading | p. 231 |
| Statistical Linearization | p. 231 |
| Multi-dimensional Regression | p. 234 |
| Limit Theorems of Probability Theory | p. 236 |
| Concepts of Probabilistic Convergence | p. 236 |
| The Law of Large Numbers | p. 237 |
| The Central Limit Theorems | p. 238 |
| Elements of Mathematical Statistics | p. 239 |
| Estimators | p. 240 |
| Testing Statistical Hypotheses | p. 241 |
| Confidence Intervals | p. 242 |
| Bibliographical Notes for Future Studies | p. 243 |
| References | p. 244 |
| Solutions | p. 247 |
| Problems of Chap.1 | p. 247 |
| Problems of Chap.2 | p. 250 |
| Problems of Chap.3 | p. 251 |
| Problems of Chap.4 | p. 253 |
| Problems of Chap.5 | p. 255 |
| Problems of Chap.6 | p. 258 |
| Problems of Chap.7 | p. 261 |
| Problems of Chap.8 | p. 264 |
| Index | p. 267 |
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