Transcript probability

Introduction to
Probabilities
Fall 2010
Dept. Electrical Engineering
National Tsing Hua University
劉奕汶
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
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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
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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%)
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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/
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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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