Probability  ( Undergraduate, 2017 Fall )
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Textbook S. Ghahramani, "Fundamentals of Probability with Stochastic Processes, 3rd Ed,"  Pearson Prentice Hall, 2005.

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Prerequisite: Calculus I & II

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Class goals:

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Learning the probability theory that describes random phenomena

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Learning probability laws and theorems for computing probabilities of events

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Learning probability methods of solving problems

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Class hours and room: 3CD5G / EC122

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Office hours: 1:30-2:300pm (Tuesday), 1:30-3:00pm (Friday) , or by appointment via emails

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TAs & TA office hours: at EC 229A

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Amir Rezapour (ce.a.rezapour@gmail.com): 3EF, 4EF

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Henry Hong (洪顥恆, henry199442.cs01@g2.nctu.edu.tw) 1B, 2C

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Grading: (tentative)

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Quizzes (in class, several times): 15%

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Homeworks: 20%

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Homework #1, due 9/29/2017 (Friday)

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Midterms (twice) 40%

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Final 25%

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Syllabus

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Preface [slides]

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Axioms of probability [slides] [noted slides]

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Sample space and events

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Axioms of probability

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Basic theorems

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Combinatorial methods [slides] [noted slides, 9/20/17]

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Counting principle

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Permutation

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Combinations

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Conditional probability and independence [slides]

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Conditional probability

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Law of multiplication

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Law of total probability

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Bayes' formula

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Independence

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Distribution functions and discrete random variables

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Random variables

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Distribution functions

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Discrete random variables

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Expectations of discrete random variables

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Variance and moments of discrete random variables

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Standardize random variables

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Special discrete distributions

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Bernoulli and binomial random variables

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Poisson random variables

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Continuous random variables

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Probability density functions

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Density function of a function of a random variable

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Expectations and variances

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Special continuous distribution

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Uniform random variables

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Normal random variable

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Bivariate distributions

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Bivariate distribution

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Independent random variables

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Conditional distributions

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More expectations and variances

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Expected values of sums of random variables

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Covariance

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Correlation

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Sums of independent random variables and limit theorem

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Markov and Chebyshev inequalities

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Law of large numbers

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Central limit theorem

-- last update: 2017/09/20