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2 Probability Theory

This chapter reviews some basic concepts of probability theory and demonstrates how they can be applied in R.

Most of the statistical functionalities in base R are collected in the stats package. It provides simple functions which compute descriptive measures and facilitate computations involving a variety of probability distributions. It also contains more sophisticated routines that, e.g., enable the user to estimate a large number of models based on the same data or help to conduct extensive simulation studies. stats is part of the base distribution of R, meaning that it is installed by default so there is no need to run install.packages("stats") or library("stats"). Simply execute library(help = "stats") in the console to view the documentation and a complete list of all functions gathered in stats. For most packages a documentation that can be viewed within RStudio is available. Documentations can be invoked using the ? operator, e.g., upon execution of ?stats the documentation of the stats package is shown in the help tab of the bottom-right pane.

In what follows, our focus is on (some of) the probability distributions that are handled by R and show how to use the relevant functions to solve simple problems. Thereby, we refresh some core concepts of probability theory. Among other things, you will learn how to draw random numbers, how to compute densities, probabilities, quantiles and alike. As we shall see, it is very convenient to rely on these routines.