PPT-Probability Theory Elements & Axioms

Probability Space of Two Die σ Algebra ℱ Sample Space Ω E514233241 Probability Measure Function P P E5 011 Probability Measure Function P . Paul Gerrard. THE. TESTING. OF. Advancing Testing Using Axioms. Agenda. Axioms – a Brief Introduction. Advancing Testing Using Axioms. First Equation of Testing. Test Strategy and Approach. Testing Improvement. Continued Fractions. Lisa Lorentzen. Norwegian University of Science and Technology. Continued fraction:. Convergence:. Möbius. transformations:. Convergence:. Catch:. L (1986). General convergence:. Phil 218/338. Welcome and thank you!. Outline. Part I: What is Bayesian epistemology?. Probabilities as . credences. The axioms of probability. Conditionalisation. Part II: Applications and problems:. : Statistics in Earth & Atmospheric Sciences. Lecture 1: Review of Probability. Instructor: Prof. Johnny Luo. www.sci.ccny.cuny.edu/~luo. Outlines. Definition of terms. Three Axioms of Probability. William W. Cohen. Machine Learning 10-605. Warmup. : Zeno’s paradox. Lance Armstrong and the tortoise have a race. Lance is 10x faster. Tortoise has a 1m head start at time 0. 0. 1. . So, when Lance gets to 1m the tortoise is at 1.1m. Overview of Probability. Shannon Quinn. CSCI 6900. Probabilistic and Bayesian Analytics. Andrew W. Moore. School of Computer Science. Carnegie Mellon University. www.cs.cmu.edu/~awm. awm@cs.cmu.edu. 412-268-7599. g. Janet Kuopus. Fall 2008 – ED311/316. My Positive Learning Story. Hiking with a Friend. She encouraged me. When it seemed I couldn’t go anymore. She believed in me. She had the patience and the time for me. The idea that underlays computational Theory. Components. Set of objects, S. Collection of functions relating objects in S. Set of axioms. that specify membership in S . specify properties of functions. calculus. 1 ≥ . Pr. (h) ≥ 0. If e deductively implies h, then Pr(h|e) = 1. .. (disjunction rule) If h and g are mutually exclusive, then . Pr. (h or g) = . Pr. (h) . Pr. (g). (disjunction rule) If h and g are . William W. Cohen. Machine Learning 10-605. Jan 19 2012. Probabilistic and Bayesian Analytics. Andrew W. Moore. School of Computer Science. Carnegie Mellon University. www.cs.cmu.edu/~awm. awm@cs.cmu.edu. Slide . 2. Probability - Terminology. Events are the . number. of possible outcome of a phenomenon such as the roll of a die or a fillip of a coin.. “trials” are a coin flip or die roll. Slide . Sixth Edition. Douglas C. Montgomery George C. . Runger. Chapter 2 Title and Outline. 2. 2. Probability. 2-1 Sample Spaces and Events . 2-1.1 Random Experiments. 2-1.2 Sample Spaces . calculus. 1 ≥ . Pr. (h) ≥ 0. If e deductively implies h, then Pr(h|e) = 1. .. (disjunction rule) If h and g are mutually exclusive, then . Pr. (h or g) = . Pr. (h) + . Pr. (g). (disjunction rule) If h and g are . 'I li :: 52 P. SUPPES pp. 229-2301. 522 P. SUPPES PROOF: Suppose not. Without loss of generality let BIA � Axiom 5 we have AIX - AnBlB and AnBlA � BIX, whence A nB/X An B/X, which is