PPT-Chapter 4: Probability: The Study of Randomness Lecture Presentation Slides

Chapter 4 Probability The Study of Randomness Lecture Presentation Slides Macmillan Learning 2017 Chapter 4 Probability The Study of Randomness 41 Randomness 42 Probability Models 43 Random Variables. . device. independent . randomness. . amplification. with . few. devices. F.G.S.L Brandao. 1. , R. . . Ramanathan. 2. . A. Grudka. 3. , K.. 4. , M.. 5. ,P.. 6. Horodeccy. 1. Department . of Computer Science, University College London. Dr. X. Topics. What Does Randomness Mean?. Randomness in . games. Generating Random Values. Random events in real life: measuring . randomness. What is Randomness?. Unpredictability?. Does it characterize a single event or a sequence of events?. the . Classical World. Kai-Min Chung . Academia . Sinica. , Taiwan. 1. Based on joint works with . Xin. Li, . Yaoyun. Shi, and . Xiaodi. Wu. Original Motivation from . 9. 0’s. Randomness is . extremely useful . 5.1.1 Random Variables and Their Distributions. A random variable is a quantity that (prior to observation) can be thought of as dependent on chance phenomena. . . Toss a coin 10 times. X=# of heads. minimal. assumptions. needed for. infinite. randomness . expansion?. Henry Yuen . (MIT). Stellenbosch, South Africa. 27 October 2015. 0. 1. 1. 0. 1. 1. 0. 1. 0. 1. 0. 0. 1. 1. 1. 0. 1. 0. 1. 1. 1. 0. Probability. The idea of probability is that chance behavior is unpredictable on the short run, but has a regular pattern in the long run…. Probability. Behavior is . random. if, while individual outcomes are uncertain, for a large number of repetitions, outcomes are regularly distributed.. by Royce Hong and Kenneth Wang. Vocabulary. Random Phenomenon. : a situation in which we know what outcomes could happen, but the particular outcome is uncertain. Probability. : the long run relative frequency of an event. Dr. Halil . İbrahim CEBECİ. Chapter . 06. Continuous. . Probability. . Distributions. a . continuous random variable. . is one that can assume an . uncountable. number of values..  . We cannot list the possible values because there is an infinite number of them.. With gratitude to the John Templeton Foundation who supported this project but is not responsible for its content. . “… if purpose is part of this universe, then randomness, by definition, is not possible. This is also one of the rationales for religious opposition to evolution, where, according to theory, (non-random) selection is applied to the results of random genetic variation.” . Feb 18. th. , 2014. IQI Seminar, Caltech. Kai-Min Chung. . IIS, . Sinica,Taiwan. Yaoyun. Shi. . University of Michigan. Xiaodi Wu. . MIT/UC Berkeley. device. …….. Ext(. x,s. i. ). Ext(x,0). Decouple. 6.4 . MATCHING PROBABILITIES . Probability is a measure of how likely an event is to occur.. Match one of the probabilities that follow with each statement about an event. (The probability . is usually . Elements of a powerful presentation. Professional presence. Clean Presentation Slides. Compelling information. Supportive Elements. Strong . Speaking. Actionable . Next Steps. Professional Presence. Wear a suit/Professional Attire. Logistics. Course Details. Lectures on . Tu. /. Th. at 1pm-2:30pm in Moore B270. Recitations on Wed at 5pm-6pm . in . Anb. 106 . Office hours on . Tu. /. Th. at . 5pm-6pm in . Anb. 106 . Lovett (IAS). Coding, Complexity and . Sparsity. workshop. August 2011. Overview. Pseudo-randomness – what? why?. Concrete examples. Local independence. Expander graphs. Small space computations.