Introduction to probability. Probability . Probability – the chance that an uncertain event will occur (always between 0 and 1) Symbols: P(event A) = “the probability that event A will occur” P(red card) = “the probability of a red card”

ByProbabilities and Proportions. Lotto. I am offered two lotto cards: Card 1: has numbers Card 2: has numbers Which card should I take so that I have the greatest chance of winning lotto?. Roulette.

ByWhy Probability? Probability theory describes the likelihood of observing various outcomes for a given population Statistics uses rules of probability as a tool for making inferences about or describing a population using data from a sample Some Concepts

ByECON 4550 Econometrics Memorial University of Newfoundland. Review of Probability Concepts. Appendix B. Adapted from Vera Tabakova’s notes . Appendix B: Review of Probability Concepts. B.1 Random Variables B.2 Probability Distributions

By11 - Markov Chains. Jim Vallandingham. Outline. Irreducible Markov Chains Outline of Proof of Convergence to Stationary Distribution Convergence Example Reversible Markov Chain Monte Carlo Methods Hastings-Metropolis Algorithm Gibbs Sampling Simulated Annealing Absorbing Markov Chains.

ByChapter 4: Reasoning Under Uncertainty. Expert Systems: Principles and Programming, Fourth Edition. Objectives. Learn the meaning of uncertainty and explore some theories designed to deal with it Find out what types of errors can be attributed to uncertainty and induction

ByLecture 10: Discrete Probability. Discrete Mathematical Structures: Theory and Applications. Learning Objectives. Learn the basic counting principles—multiplication and addition Explore the pigeonhole principle Learn about permutations Learn about combinations. Learning Objectives.

ByP robability Models & Applications. Tutorial 3. Poisson Distribution . A random variable X, taking on one of the values 0, 1, 2, … , is said to be a Poisson random variable with parameter λ, if for some λ> 0, . Approximate Binomial by Poisson Distribution .

ByChapter 5. Markov processes Run length coding Gray code. Markov Processes. Transition Graph. Transition Matrix. Weather Example : Let ( j = 1). Think: a means “fair” b means “rain” c means “snow”. ½. next symbol. b. ⅓. ⅓. c u r r e n t s t a t e. ¼. ⅓ ⅓ ⅓

ByOdds and Relative Risk. Note: this PowerPoint presentation is unfinished. Probabilities. Probabilities. Suppose that in 2005-06 a particular 2-year college graduated 300 students from a cohort of 700 students. In this case the probability of graduating is:. Probabilities.

ByChapter 6 - Probability. Math 22 Introductory Statistics. Simulating Repeated Coin Tosses. Simulation with the TI – 83 Empirical Probability (Observed Probability) – The probability of a specific event as it was observed in an experiment.

ByBayesian Networks. Introduction. A problem domain is modeled by a list of variables X 1 , …, X n Knowledge about the problem domain is represented by a joint probability P(X 1 , …, X n ). Introduction. Example: Alarm

ByCapital Allocation using the Ruhm-Mango-Kreps Algorithm. David L. Ruhm, FCAS Enterprise Risk Management Symposium Session CS-13: Risk-Adjusted Capital Allocation July 30, 2003 Washington, DC. The Capital Allocation Problem.

ByThree Common Misinterpretations of Significance Tests and p-values. 1. The p-value indicates the probability that the results are due to sampling error or “chance.” 2. A statistically significant result is a “reliable” result.

ByURBDP 591 A Lecture 10: Causality. Objectives Internal Validity Threats to Internal Validity Causality Bayesian Networks. Internal validity. The extent to which the hypothesized relationship between 2 or more variables is supported by evidence in a given study. Validity.

ByEvents and their probability Basic relationships of probability Conditional probability. Events and their probabilities. An event is a collection of sample points. The probability of an event is equal to the sum of the probabilities of the sample points in the event.

By3.2 Conditional Probability & the Multiplication Rule. Statistics Mrs. Spitz Fall 2008. Objectives/Assignment. How to find the probability of an even given that another event has occurred. How to distinguish been independent and dependant events.

ByApplicable Mathematics “Probability”. www.mathxtc.com. Definitions. Probability is the mathematics of chance. It tells us the relative frequency with which we can expect an event to occur. The greater the probability the more likely the event will occur. .

ByCOMPLETE BUSINESS STATISTICS. by AMIR D. ACZEL & JAYAVEL SOUNDERPANDIAN 6 th edition. Chapter 2. Probability. Probability. 2. Using Statistics Basic Definitions: Events, Sample Space, and Probabilities Basic Rules for Probability Conditional Probability Independence of Events

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