A Note on the Concept of Independence
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Elart von Collani
Abstract
In 1933 A.N. Kolmogorov's famous essay Grundbegriffe der Wahrscheinlichkeitsrechnung was published by the publisher Julius Springer in Berlin. It contained an axiomatization of probability theory and led to an unimagined upturn of probability theory and its application. Especially the effect on application must surprise because based on the the axioms, probability theory had become a genuine part of mathematics without any concrete real-world meaning. Kolmogorov states himself about the field of probabilities: “What the elements of this set represent is of no importance in the purely mathematical development of the theory of probability.” In his treatise Kolmogorov also deals with the concept of independence and introduces it as a purely mathematical quantity without regarding any real-world meaning. In this paper it is shown that the mathematical concept of independence of events is inappropriate from a more realistic point of view.
© Heldermann Verlag
Articles in the same Issue
- Transient Analysis of Multistage Degraded Systems with Partial Repairs of General Distribution Modeled by Erlang-k Distribution
- A Practical Procedure for Developing p-Charts
- Posterior Distribution and Loss Functions for Parameter Estimation in Weibull Processes
- Combined CUSUM–Shewhart Schemes for Binomial Data
- A Goodness of Fit Approach to NBURFR and NBARFR Classes
- Control Charts for the Log-Logistic Distribution
- Stability Index of Stochastic Processes: The Statistical Process Control Approach
- Multivariate Max-Chart
- An Optimization Methodology for Condition Based Minimal and Major Preventive Maintenance
- Multivariate Diagnostic Tests: A Review of Different Methods
- A Note on the Concept of Independence
Articles in the same Issue
- Transient Analysis of Multistage Degraded Systems with Partial Repairs of General Distribution Modeled by Erlang-k Distribution
- A Practical Procedure for Developing p-Charts
- Posterior Distribution and Loss Functions for Parameter Estimation in Weibull Processes
- Combined CUSUM–Shewhart Schemes for Binomial Data
- A Goodness of Fit Approach to NBURFR and NBARFR Classes
- Control Charts for the Log-Logistic Distribution
- Stability Index of Stochastic Processes: The Statistical Process Control Approach
- Multivariate Max-Chart
- An Optimization Methodology for Condition Based Minimal and Major Preventive Maintenance
- Multivariate Diagnostic Tests: A Review of Different Methods
- A Note on the Concept of Independence
