3 Exploring probability distributions and conditional probabilities

 

This chapter covers

  • Probability distributions
  • Probability computations
  • Conditional probabilities

In statistics and especially probability theory, understanding the behavior of random variables is just the beginning of a fascinating journey into the worlds of uncertainty and prediction. As we dive deeper into this subject, we arrive at a crucial inflection point: the exploration of probability distributions and conditional probability computations.

This chapter builds on the foundation established in chapter 2, where we introduced the concept of random variables and their properties. With this groundwork in place, we now embark on an in-depth exploration of four common probability distributions: normal, binomial, uniform, and Poisson.

Random variables serve as the bedrock on which probability distributions are constructed, allowing us to model and analyze the likelihood of various outcomes in a systematic manner. By examining specific probability distributions such as the normal distribution, which describes continuous phenomena like heights and weights, and the binomial distribution, which deals with discrete events like coin flips, we gain a deeper appreciation for the diverse ways in which uncertainty manifests itself in the real world.

3.1 Probability distributions

3.1.1 Normal distribution

3.1.2 Binomial distribution

3.1.3 Discrete uniform distribution

3.1.4 Poisson distribution

3.2 Probability problems

3.2.1 Complement rule for probability

3.2.2 Quick reference guide

3.2.3 Applied probability: Examples and solutions

3.3 Conditional probabilities

3.3.1 Examples

3.3.2 Conditional probabilities and independence

3.3.3 Intuitive approach to conditional probability

3.3.4 Formulaic approach to conditional probability

Summary