Statistical Theory

Book excerpt: Fundamental calculus of probabilities -- Some fundamental applications of the calculus of probabilities -- Graphical and tabular representation of observations -- Definitions and fundamental properties of empirical distributions -- Definitions and fundamental properties of theoretical distributions -- The normal distribution -- Skew distributions -- Some limit theorems and sampling distributions -- The distribution of the mean -- The X2-distribution -- The distribution of the variance -- The distribution of the range -- Statistical control -- The distribution of the variance ratio -- The t-distribution -- Analysis of variance -- Designs of sampling investigations and experiments -- Linear regression analysis with one independent variable -- The two-dimensional normal distribution -- Multi-dimensional correlation and regression -- The binomial distribution -- The poisson distribution -- The multinomial distribution and the X2-test -- Sequential analysis -- The main points of a statistical analysis.