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

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.