Mathematical induction: Theory and simple proofs
1 Lecturer in Science Department, Karnataka Government Polytechnic Mangalore, Karnataka, India.
2 Senior scale lecturer in science Government polytechnic, chamarajanagar-571313, Karnataka, India.
Research Article
World Journal of Advanced Research and Reviews, 2022, 17(01), 1396-1399
Publication history:
Received on 13 December 2022; Revised 25 December 2022; accepted on 05 January 2023
Abstract:
Big Data Analytics involves processing, analyzing, and interpreting massive datasets to extract meaningful insights, optimize decision-making, and enhance predictive capabilities. Probability distributions serve as fundamental tools in this domain, providing structured frameworks for modeling data variability, identifying underlying patterns, and improving statistical inference. This paper explores the critical role of probability distributions in Big Data Analytics, focusing on their applications in data modeling, statistical hypothesis testing, and machine learning algorithms. The study provides a comprehensive overview of key probability distributions, including normal, exponential, Poisson, binomial, and power-law distributions, highlighting their mathematical foundations and real-world applications. Furthermore, the paper discusses how these distributions aid in anomaly detection, predictive modeling, and risk assessment in large-scale data environments. The integration of probability models with machine learning techniques is also examined, showcasing their impact on classification, clustering, and regression tasks. Figures, tables, and bar charts illustrate the significance of probability models in efficiently handling vast and complex datasets, emphasizing their role in enhancing accuracy, scalability, and computational efficiency in Big Data applications.
Keywords:
Mathematical; Induction Principle of Mathematical Induction (PMI); Base Case; Inductive Step Strong ; Induction Structural; Induction Proof Techniques
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Copyright © 2023 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution Liscense 4.0