Cumulative Distribution Function: A Mathematical Approach to Probabilistic Modeling in Robotics
Giới thiệu về sách nói này
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.
