Random variables and their distributions
In this chapter, we introduce random variables, an incredibly useful concept that simplifies notation and expands our ability to quantify uncertainty and summarize the results of experiments. Random variables are essential throughout the rest of this book, and throughout statistics, so it is crucial to think through what they mean, both intuitively and mathematically.
3.1 Random variables
To see why our current notation can quickly become unwieldy, consider again the gambler’s ruin problem from Chapter 2. In this problem, we may be very interested in how much wealth each gambler has at any particular time. So we could make up notation like letting Ajk be the event that gambler A has exactly ...