Cumulative Distribution Function - A Mathematical Approach to Probabilistic Modeling in Robotics
Fouad Sabry
Casa editrice: One Billion Knowledgeable
Sinossi
1: Cumulative Distribution Function – Introduces the CDF and its foundational role in probability. 2: Cauchy Distribution – Examines this key probability distribution and its applications. 3: Expected Value – Discusses the concept of expected outcomes in statistical processes. 4: Random Variable – Explores the role of random variables in probabilistic models. 5: Independence (Probability Theory) – Analyzes independent events and their significance. 6: Central Limit Theorem – Details this fundamental theorem’s impact on data approximation. 7: Probability Density Function – Outlines the PDF and its link to continuous distributions. 8: Convergence of Random Variables – Explains convergence types and their importance in robotics. 9: MomentGenerating Function – Covers functions that summarize distribution characteristics. 10: ProbabilityGenerating Function – Introduces generating functions in probability. 11: Conditional Expectation – Examines expected values given certain known conditions. 12: Joint Probability Distribution – Describes the probability of multiple random events. 13: Lévy Distribution – Investigates this distribution and its relevance in robotics. 14: Renewal Theory – Explores theory critical to modeling repetitive events in robotics. 15: Dynkin System – Discusses this system’s role in probability structure. 16: Empirical Distribution Function – Looks at estimating distribution based on data. 17: Characteristic Function – Analyzes functions that capture distribution properties. 18: PiSystem – Reviews pisystems for constructing probability measures. 19: Probability Integral Transform – Introduces the transformation of random variables. 20: Proofs of Convergence of Random Variables – Provides proofs essential to robotics reliability. 21: Convolution of Probability Distributions – Explores combining distributions in robotics.
