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Cumulative Distribution Function - A Mathematical Approach to Probabilistic Modeling in Robotics - cover

Cumulative Distribution Function - A Mathematical Approach to Probabilistic Modeling in Robotics

Fouad Sabry

Publisher: One Billion Knowledgeable

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Summary

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.
Available since: 12/16/2024.
Print length: 422 pages.

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