Elements of Probability Theory

Elements of Probability Theory presents the methods of the theory of probability. This book is divided into seven chapters that discuss the general rule for the multiplication of probabilities, the fundamental properties of the subject matter, and the classical definition of probability. The introductory chapters deal with the functions of random variables; continuous random variables; numerical characteristics of probability distributions; center of the probability distribution of a random variable; definition of the law of large numbers; stability of the sample mean and the method of moments; and Chebyshev's theorem. The next chapters consider the limit theorem of de Moivre-Laplace and the solution of two fundamental problems in the theory of errors. The discussion then shifts to the best linear approximation to the regression function. The concluding chapters look into the central limit theorem of Lyapunov and the significance of the value of the coefficient of correlation. The book can provide useful information to the statisticians, students, and researchers.