ABSTRACT
The theory of probability and statistics is concerned with situations in which an observation is made and which contain an element of inherent variability out with the observer's control. In the sense an observation gives information about the true distribution. Possible observations in a situation under investigation will be represented in a mathematical set or space called a sample space. It is not necessary that there be a one-to-one correspondence between elements of a sample space and possible observations. To define a probability distribution on a sample space it is not necessary to define the probability of every event. The distribution is completely defined by defining the probabilities of a sufficiently wide class of events, and then the rules or axioms of a probability distribution may be used to deduce the probabilities of events outside this class. Indeed it is the case that almost all situations in which observations are taken contain this element of variability.
