It may occur frequently that in performing an experiment one is not interested directly in the entire sample space or in events defined over the sample space. For example, suppose that the experiment which measures the times of the first arrival on 2 days was performed to determine at what time to open the store. Prior to performing the experiment, the store owner decides that if the average of the arrival times is greater than an hour, therefore he will not open his store until 10 A.M. (9 A.M. being the previous opening time).
In this experiment the average of the arrival times X is a random variable. Notationally, random variables will be characterised by capital letters, and the values the random variable takes on will be denoted by lower letters. Actually, to be precise, X should be written as X(w), where w is any point shown in the previous square because X is a function.
The random variables can be described as follows.