In this chapter we explore the basic types of probability distributions, and the ways that distributions can be defined using density functions, distribution functions, and quantile functions. We also study the relationship between the distribution of a random vector and the distributions of its components, and how the distribution of a random variable changes when the variable is transformed. Finally, we study convergence in distribution, one of the most important types of convergence.
Nothing can permanently please which does not contain in itself the reason why it is so and not otherwise.--Samuel Taylor Coleridge