An Essay on the Prerequisites for the Probability Theory

The probability calculus and statistics as well permeate nearly every discipline and professional sector, while no theories underpinning this wide spreading field reached universal consensus so far. The probability interpretations present irreconcilable traits, so the concept of probability is still substantially unclear. Purpose of this work: The present paper intends to demonstrate how the different models of probability constitute the facial problem which conceals another hidden and more fundamental question. Method: We show how authors do not agree with the concept of probability P and moreover they have different ideas about the precise object qualified by P, which has priority from the point of logic. It is clear how the element X measured by P(X) influences its meaning. In consequence of the conflicting opinions, theorists tend toward a compromise. They use the outcome or result of an experiment as the argument X of P(X) and represent X as a subset of the event space. This paper suggests replacing the outcome-subset with the event-triad E, which provides a comprehensive mathematical support. Results: The last section shows how the triadic model is formally consistent with the conventional theories and can integrate the conflicting views on probability. This unifying result can help mathematicians to go beyond the present theoretical deadlock. In summary, this paper advocates a more explicit notation system for probability and points out how probability can be ambiguous without rigorous specification of the sample space and the experiment in general.

An Essay on the Double Nature of the Probability

Classical statistics and Bayesian statistics refer to the frequentist and subjective theories of probability respectively. Von Mises and De Finetti, who authored those conceptualizations, provide interpretations of the probability that appear incompatible. This discrepancy raises ample debates and the foundations of the probability calculus emerge as a tricky, open issue so far. Instead of developing philosophical discussion, this research resorts to analytical and mathematical methods. We present two theorems that sustain the validity of both the frequentist and the subjective views on the probability. Secondly we show how the double facets of the probability turn out to be consistent within the present logical frame.

Four Common Properties of Repairable Systems Calculated with the Boltzmann-Like Entropy

Gnedenko, the father of the modern Reliability Theory, first derived some fundamental properties of reliable systems following rigid deductive logic. This paper shares the deductive method and infers four principal properties of repairable/maintainable systems using the Boltzmann-like entropy. In particular we calculate the reparability function and next discuss the physical meanings of the formal results. Lastly we comment on the broad range of applications and researches which can relate to this study.

How Semiotics Can Improve Our Knowledge on Computing

Several computer theorists and professionals share the concepts of ＂signifier＂ and ＂signified＂ in intuitive terms but are often unfamiliar with semiotics. There is a special digital divide between semiotics and the technology, because the semiotic notions are usually expressed through verbal expressions instead engineers use the mathematical language. In the first step, the present study suggests the formal descriptions of the signifier and the signified. In the second step, we show how these formal definitions are able to justify the hardware structure of a computer system, and even other properties of computing which are currently presented on the as-is basis. Concluding, the basic concepts of semiotics can unveil intriguing aspect of information technology