Probability, conditional probability, independence: 1.1 Experiments / Models, deterministic and non-deterministic models. Random experiment, concept of statistical regularity. 1.2... Probability, conditional probability, independence: 1.1 Experiments / Models, deterministic and non-deterministic models. Random experiment, concept of statistical regularity. 1.2 Definitions of - (i) Sample space, (ii) Discrete sample space: finite and countably infinite, (iii) Continuous sample space, (iv) Event, (v) Elementary event, (vi) Complement of an event, (vii) Certain event, (viii) Impossible event. Concept of occurrence of an event. 1.3 Algebra of events and its representation in set theory notation. Classical definition of probability and its limitations. Probability model, equiprobable and non-equiprobable sample space. 1.4 Axiomatic definition of probability, theorems of probability, computation of probability of an event conditional probability of an event. 1.5 Independence of two events. Pair-wise independence and mutual independence for three events. Multiplication theorem P (A∩ B) = P(A) · P(B|A) and its generalization. 1.6 Bayes’ Theorem Partition of the sample space. Proof of Bayes’ theorem, Applications of Bayes’ theorem in real life.
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The question is a comprehensive outline of topics related to probability theory. It encompasses concepts such as random experiments, sample spaces, events, and definitions related to probabilities, including conditional probability, independence, and Bayes’ theorem. It seems to be prompting an explanation or discussion on each of these subtopics.
Answer
Search results contain detailed educational material on probability theory, covering key concepts like sample spaces, events, and Bayes' Theorem.
The web search results provide educational material on probability concepts, including sample spaces, events, and theorems like Bayes' Theorem. Useful resources can be found at universities or educational platforms.
Answer for screen readers
The web search results provide educational material on probability concepts, including sample spaces, events, and theorems like Bayes' Theorem. Useful resources can be found at universities or educational platforms.
More Information
Probability theory extensively deals with the likelihood of events within a model. Key topics include definitions of sample spaces and events, probability axioms, and concepts such as independence and conditional probability.
Sources
- Probability theory course material - Studocu - studocu.com
- Probability and Statistics for Data Science - cims.nyu.edu
- Chapter 2: Probability - stat.auckland.ac.nz
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