Probability and Statistics: Volume I

1 Censuses.- 1.1. Census of Two Qualitative Characteristics.- 1.2. A Census of Quantitative Characteristics.- 1.3. First Definitions of Discrete Probabilities.- 1.4. Pairs of R.V.'s and Correspondence Analysis.- 2 Heads or Tails. Quality Control.- 2.1. Repetition of n Independent Experiments.- 2.2. A Bernoulli Sample.- 2.3. Estimation.- 2.4. Tests, Confidence Intervals for a Bernoulli Sample, and Quality Control.- 2.5. Observations of Indeterminate Duration.- 3 Probabilistic Vocabulary of Measure Theory. Inventory of the Most Useful Tools.- 3.1. Probabilistic Models.- 3.2. Integration.- 3.3. The Distribution of a Measurable Function.- 3.4. Convergence in Distribution.- 4 Independence: Statistics Based on the Observation of a Sample.- 4.1. Sequence of n Observations-Product Measure Spaces.- 4.2. Independence.- 4.3. Distribution of the Sum of Independent Random Vectors.- 4.4. A Sample from a Distribution and Estimation of this Distribution.- 4.5. Nonparametric Tests.- 5 Gaussian Samples, Regression, and Analysis of Variance.- 5.1. Gaussian Samples.- 5.2. Gaussian Random Vectors.- 5.3. Central Limit Theorem on ?k.- 5.4. The X2 Test.- 5.5. Regression.- 6 Conditional Expectation, Markov Chains, Information.- 6.1. Approximation in the Least Squares Sense by Functions of an Observation.- 6.2. Conditional Expectation-Extensions.- 6.3. Markov Chains.- 6.4. Information Carried by One Distribution on Another.- 7 Dominated Statistical Models and Estimation.- 7.1. Dominated Statistical Models.- 7.2. Dissimilarity in a Dominated Model.- 7.3. Likelihood.- 8 Statistical Decisions.- 8.1. Decisions.- 8.2. Bayesian Statistics.- 8.3. Optimality Properties of Some Likelihood Ratio Tests.- 8.4. Invariance.- Notation and Conventions.