Random variables, means, and variance
Informally, we can say that random variables are functions that map outcomes to numerical values. Since the probability measure assigns probabilities to outcomes and events, we may define the probability that a random variable equals certain values. The technical definition is as follows.
Definition – random variable
A function X: S → R, where R is a discrete set, is a discrete random variable (RV).
Important Note
The other main class of RVs is continuous RVs, which take values in R or some other uncountable set instead of just a discrete set, but they are outside the scope of this book.
Example – data transfer errors
Data transferred over digital communication channels are, at the lowest level, a stream of binary digits. Sometimes there can be noise or other distortions that cause errors in their transmission. It is important to quantify the errors, but it is random, so the best we can do is estimate the...