Introduction to Probabilities
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Transcript of Introduction to Probabilities
Introduction to Probabilities
Fall 2010Dept. Electrical Engineering
National Tsing Hua University
劉奕汶
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What is probability?
• Literally, how probable an event is to occur.– We live in a random world– Relative-frequency interpretation
• 機率/概率/或然率– This interpretation is problematic
• Involved law of large number• Not all experiments could be repeated • Not all repeating processes have convergent frequency
– Axiomatic approach
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A bit of History
• 3500 B.C., Egyptians used bones to gamble– Since then, dice, playing cards, mahjong, etc.
• 15-16th centuries: Italy (Galilei et al.)
• 17-18th centuries: Western-central Europe– Pascal, Fermat, Laplace, Poisson, Gauss– Huygens (1629-1695) On Calculations in Games of Chance
• 19-20th : Russia– 1900: Hilbert’s 23 problems– 1933: Kolmogorov: probability theory axiomatized
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Probability in EE/CS
• Signal processing– “Signal” = Random Process– Random because of noise and uncertainty
• Machine learning– Natural language processing– Pattern recognition
• Communication– Source coding– Channel coding– Modulation and estimation
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Probability in Finance/Economics
• Investment / Gambling– Portfolio theory
• Advertisement / Pricing
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Probability in Physics (i)
• Statistical mechanics– Equilibrium– Entropy and 2nd law of thermodynamics– Definition of temperature
Probability in Physics (ii)
• Quantum mechanics– Schrödinger’s wave function– “Measurement makes reality”
• The paradox of Schrödinger’s cat• Einstein’s famous comment
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Probability in Biomedicine
• Genomics
• Proteomics
• Neuroscience
• Ecology
• Epidemiology
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Probability and Statistics
• Law of Large Number
• Central Limit Theorem– Why Gaussian distribution is “Normal”
• Counter-example: stock market
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Syllabus• Textbook: S. Ghahramani, Fundamentals of Probability: with
stochastic processes, 3rd Edition– Chapters 1-3: probability space – Chapters 4-5: discrete random variables– Chapter 6: Continuous random variables– Midterm exam (35%)– Chapters 7: continuous random variables II– Chapters 8: bivariate distributions– Chapter 10-11: advanced topics (Correlations, LLN, CLT, etc)– * Measure theory and axioms of probability– Final exam (35%)
• A4 double-side cheat sheet permitted for both exams – 6 homework assignments (30%)
• Office hours: Monday 5-6 pm, Rm 704B• Website: http://www.ee.nthu.edu.tw/ywliu/ee3060/
Statistics of last semester’s grades (N = 37)
• 期中考 : M = 51.4, SD = 7.9
• 期末考 : M = 49.3, SD = 10.8
• 總成績 : M = 78, SD = 11– 36 passed, 1 failed. – 4 scored 90 or above (A+)
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