Statistical Inference: A Short Course

4.1 Set Notation

This section offers a brief review of set notation and concepts (readers familiar with this material showed proceed to the next section). These (set) notions are important in that they offer the reader a way of “thinking” or a way to “organize information”. As we shall see shortly, only “events” have probabilities associated with them, and these events are easily visualized/described and conveniently manipulated via set operations.

Let us define a set as a collection or grouping of items without regard to structure or order—we have an amorphous group of items. Sets will be denoted using capital letters (A, B, C, . . .). An element is a member of a set. Elements will be denoted using small-case letters (a, b, c, . . .). A set is defined by listing its elements. If forming a list is impractical or impossible, then we can define a set in terms of some key property that the elements, and only the elements, of the set possess. For instance, the set of all odd numbers can be defined as . Here n is a representative member of the set N and the vertical bar reads “such that.”

If an element is a member of set , we write (element inclusion); if is not a member of then (we negate ...