Econometric Theory/Sample Points, Sample Space and Events

The population or the sample space refers to the set of all possible outcomes of an experiment that is random. If you toss a coin there are two possible outcomes: head (H) or tail (T). If you toss two coins, there are four outcomes: HH, HT, TH and TT, where the first letter refers to the outcome of the first tossing and the second to that of the second tossing. Each outcome is called a sample point.

An event is a subset of a sample space. If we want to list all sample points with the occurrence of at least one H, we have HH, HT and TH. Any events are called mutually exclusive if, for any one trial of the experiment, the occurrence of one event implies the non-occurrence of the other event. For instance, if we got a head on one occasion, we could not simultaneously get a tail. Note: To say that any 2 events are independent means something else entirely.

Events are exhaustive if there is no other possible event. For instance, the events two heads (HH), one head and one tail (HT and TH), and two tails (TT) are all possible outcomes if tossing the coin twice. Thus, the list of events is exhaustive.