Computation of probability by direct enumeration of cases. Theorems of total and compound probability. Repeated trials. Probabilities of hypotheses and bayer' theorem. Use of difference equations in solving problems of probability. Bernoulli's theorem. Approximate evaluation of probabilities in bernoullian case. Further considerations on games of chance. Mathematical expectation. The law of large numbers. Application of the law of large numbers. Probabilities in continuum. The general concept of distribution. Fundamental limit theorems. Normal distribution in two dimensions. Limit theorem for sums of independent vectors. Origin of normal correlation. Distribution of certain functions of normally distributed variables. Euler's summation formula - stirling's formula - some definite integrals. Method of moments and its applications.Computation of probability by direct enumeration of cases.
|Title||:||Introduction to Mathematical Probability|
|Author||:||James Víctor Uspensky|