PPT-Chapter 14: From Randomness to Probability

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. How can we draw the line?. Taner Edis. Department . of Physics,. . Truman . State . University. Supernatural fiction. Stories of ghosts, gods, spirits, magic, the occult.. Personality and agency (“spirit”) somehow fundamental to how the world works.. 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 . th. edition – For AP*. STARNES, YATES, MOORE. Chapter 5: Probability: What are the Chances?. Section 5.1. Randomness, Probability, and Simulation. Chapter 5. Probability: What Are the Chances?. 5.1 . Follow-Up:. Further into Python. Part 3: . Random. Numbers. Part 3: . “Random”. Numbers. Part 3: . Pseudo. -Random. Numbers. Why Random Numbers?. Traditional use: cryptography. http://www.diablotin.com/librairie/networking/puis/figs/puis_0604.gif. 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.. Shachar. Lovett (IAS). Coding, Complexity and . Sparsity. workshop. August 2011. Overview. Pseudo-randomness – what? why?. Concrete examples. Local independence. Expander graphs. Small space computations. Randomness. ？. 隨機是指缺乏模式及可預測性的. 事件. e.g.. . 擲骰、六合彩、粒子運動等. 甚麼是機率. Probability. ？. 機率是用以描述隨機事件結果的數學. 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. Chapter 4: Probability: The Study of Randomness Lecture Presentation Slides Macmillan Learning © 2017 Chapter 4 Probability: The Study of Randomness 4.1 Randomness 4.2 Probability Models 4.3 Random Variables Nava . Schulmann. 13/04/2015. Past. I have a Ph.D. in Physics focused on elastic properties of polymers.. Present. I am a post-doctoral . fellow at . the . Science-Teaching department of the Weizmann Institute of Science, Israel. '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 Lovett (IAS). Coding, Complexity and . Sparsity. workshop. August 2011. Overview. Pseudo-randomness – what? why?. Concrete examples. Local independence. Expander graphs. Small space computations.