2.1 The Axiomatic Approach The axiomatic approach to probability proceeds from a set of axioms(accepted without questioning as obvious), which are based on many centuries of human experience, and the subsequent development is built deductively using formal logical arguments, like any other part of mathematics such as geometry or linear algebra. In mathematics an axiomatic system is required to be complete, non redundant and consistent. By complete we mean that the set of axioms postu- lated should enables us to prove every other theorem in the theory in question using the axioms and mathematical logic. The notion of non-redundancy refers to the impossibility of deriving any axiom of the system from the other axioms Consistency refers to the non- contradictory nature of the axioms a probability model is by construction intended to be a description of a chand mechanism giving rise to observed data. The starting point of such a model is provided by the concept of a random experiment describing a simplistic and idealized process giving rise to observed data. The starting point of such a model is provided by the concept of a random erperiment describing a simplistic and idealized process giving rise to the observed data Definition 1 A random experiment, denoted by &, is an experiment which satisfies the fol- wing conditions (a) all possible distinct outcomes are known a priori (b) in any particular trial the outcomes is not known a priori; and (c)it can be repeated under identical conditions The axiomatic approach to probability theory can be viewed as a formalization of the concept of a random experiment. In an attempt to formalize condition(a) all possible distinct outcome are known a priori, Kolmogorov devised the set s which included "all possible distinct outcome" and has to be postulated before the experiment is performed Definition 2 The sample space, denoted by S, is defined to be the set of all possible outcome of the experiment 8. The elements of S are called elementary events2.1 The Axiomatic Approach The axiomatic approach to probability proceeds from a set of axioms (accepted without questioning as obvious), which are based on many centuries of human experience, and the subsequent development is built deductively using formal logical arguments, like any other part of mathematics such as geometry or linear algebra. In mathematics an axiomatic system is required to be complete, non − redundant and consistent. By complete we mean that the set of axioms postu￾lated should enables us to prove every other theorem in the theory in question using the axioms and mathematical logic. The notion of non-redundancy refers to the impossibility of deriving any axiom of the system from the other axioms. Consistency refers to the non- contradictory nature of the axioms. A probability model is by construction intended to be a description of a chance mechanism giving rise to observed data. The starting point of such a model is provided by the concept of a random experiment describing a simplistic and idealized process giving rise to observed data. The starting point of such a model is provided by the concept of a random experiment describing a simplistic and idealized process giving rise to the observed data. Definition 1: A random experiment, denoted by E, is an experiment which satisfies the fol￾lowing conditions: (a) all possible distinct outcomes are known a priori; (b) in any particular trial the outcomes is not known a priori; and (c) it can be repeated under identical conditions. The axiomatic approach to probability theory can be viewed as a formalization of the concept of a random experiment. In an attempt to formalize condition (a) all possible distinct outcome are known a priori, Kolmogorov devised the set S which included ”all possible distinct outcome” and has to be postulated before the experiment is performed. Definition 2: The sample space, denoted by S, is defined to be the set of all possible outcome of the experiment E. The elements of S are called elementary events. 5