Types of Random Variables

Having defined a random variable in general, the chapter now separates every random variable into exactly one of two families based on the nature of its range: discrete random variables, whose possible values can be counted out one by one (finite or countably infinite), and continuous random variables, whose possible values fill up an entire interval of real numbers and so cannot be listed one at a time. This split matters because the two families are described by different mathematical machinery later in the chapter — a discrete random variable by a probability mass function (its probabilities can simply be listed against its values), a continuous random variable by a probability density function (probabilities come from areas u …