7 Basics of Probability Theory
Probability is the basic ingredient of statistical inference.
In this chapter, we will cover the very basics of probability theory. We will visit its axiomatic definition and some common interpretations in Section 7.1, where we also start with the main mental exercise of this section: seeing how probability distributions can be approximately represented by samples. We will cover important concepts such as joint and marginal probability in Section 7.2. This paves the way for learning about conditional probability and Bayes rule in Section 7.3. Section 7.4 introduces the notion of a random variable. Finally, Section 7.5 briefly covers how information about common probability distributions can be accessed in R.
The learning goals for this chapter are:
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become familiar with the notion of probability and also:
- its axiomatic definition
- the notion of joint, marginal and conditional probability
- understand and apply Bayes rule
- get comfortable with random variables
- understand how probability distributions are approximately represented by samples
- become able to use R’s built-in probability distributions