Discrete Random Variables

A random variable is said to be discrete if the number of its possible values is finite or countably infinite. By long-standing convention the values of a discrete random variable are usually taken to be non-negative integers, $\{0, 1, 2, \ldots\}$, though in general they can be any real numbers, positive, negative, integer or fractional (as later examples in section 7.3 show). Discrete random variables arise wherever the underlying quantity is obtained by counting: the number of children in a family, the number of patients in a hospital ward on a given day, the number of cars sold by a dealer in a month, or even the number of stars in the sky — however large, each …