ABSTRACT
The chapter describes such concepts of probability calculus which are needed in later chapters. A total of 26 short examples are included to illustrate the concepts using R-scripts and figures. First, concepts related to univariate random variables are presented, including the distribution and density functions of random variables, and the expected value and variance. These concepts are further extended to multivariate random variables, where also covariance and correlation are defined. Multivariate random variables can be described in terms of the joint, marginal and conditional distributions. These can be summarized using conditional and marginal expectations and variances, which are based on matrix notations. Calculation rules for the expected value, variance and covariance are summarized in one page for easy reference. The quantile function, weighted and censored distributions, and compound distributions are also defined. The normal, t, chi-square and F distributions, which are needed in hypothesis testing, are introduced and their relationship are described. The chapter also gives a short introduction to stochastic and spatial processes.
