Normal Distribution In Historio-Philosophic Context
In general the set-up of the research work has a logical intention. That is the chapters and their respective sections are logically arranged so that one can read and arrive at the results inductively or deductively. Chapter one gives a preliminary background on the important research questions, namely, the schematic discernment of statistical and probabilistic research works and method of approach at University of Nairobi, and the characterization of normal distribution in Hilbert Space. Chapter two focuses on the historio-philosophic development of probability and statistical thoughts and theories. As a concluding remark on this chapter, a tentative conclusion on the historio-philosophic approach of the Statistical Section of Mathematics at University of Nairobi on the mathematical probability and statistics is given. In chapter three first we come across the historical context of normal distribution and its philosophic applications. Furthermore, different approaches in defining and analyzing the unique properties of normal distribution are given: modem and classical approaches. In addition, different models of investigations, like De Moivre-Laplace method, Adrians method, Hegen's hypothesis and so on, are studied in deriving the normal distribution. Also, The central importance of normal distribution in.. probabilistic and statistical studies is illustrated by the relationship between normal distribution with discrete and continuous distribution as well as properties of pure and applied mathematics; normal distribution is analyzed using the number theory and Maxwell's distribution of velocities and law of error. The highly developed mathematical methodologies, theorems and techniques of the characterization of normal distribution are elaborated. Using these techniques the theory of normal distribution in Hilbert space is studied. Chapter four develops the central issue of the statement of problem logically. That is, first after a brief historical analysis, the fundamental definitions and properties of Hilbert space are described. Then the geometry of Hilbert space with operator theory are presented. Finally, the necessary properties and theorems of normal distribution in Hilbert space are clarified.