Probability and Random Variables (2012) by Elif Uysal-Bıyıkoğlu at METU

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source: METUOpenCourseWare    2013年1月30日
EE230 - Probability and Random Variables
Axiomatic definition of probability spaces. Combinatorial methods. Conditional probability; product spaces. Random variables; distribution and density functions; multivariate distribution; conditional distributions and densities; independent random variables. Functions of random variables; expected value, moments and characteristic functions.
OpenCourseWare [ http://ocw.metu.edu.tr ]
For Lecture Notes: http://ocw.metu.edu.tr/course/view.ph...

Week 2 - Lecture 1 Probability Spaces; Axioms and properties or probability 46:27
Week 2 - Lecture 2 Discrete and Continuous Probability Laws, Conditional Probability 46:58
Week 2 - Lecture 3 Discrete and Continuous Probability Laws, Conditional Probability 40:36
Week 3 - Lecture 1 Total Probability Theorem, Bayes's Rule 46:04
Week 3 - Lecture 2 Independence, Conditional Independence 48:51
Week 3 - Lecture 3 Independence, Conditional Independence 41:35
Week 3 - Lecture 3 Independence, Conditional Independence 41:35
Week 4 - Lecture 1 Independent Trials, Counting 53:01
Week 4 - Lecture 2 Discrete Random Variables 52:40
Week 4 - Lecture 3 Discrete Random Variables 29:30
Week 5 - Lecture 1 Expectation and Variance 44:48
Week 5 - Lecture 2 Properties of Expectation and Variance, Joint PMFs 39:31
Week 5 - Lecture 3 Properties of Expectation and Variance, Joint PMFs 35:37
Week 6 - Lecture 1 Conditional PMFs 47:59
Week 6 - Lecture 2 Conditioning one Random Variable on another; conditional expectation 50:10
Week 6 - Lecture 3 Conditioning one Random Variable on another; conditional expectation 42:47
Week 7 - Lecture 1 Iterated Expectation; Independence of a random variable from an event 43:18
Week 7 - Lecture 2 Independence of Random Variables 39:24
Week 7 - Lecture 3 Independence of Random Variables 32:50
Week 8 - Lecture 1 Continuous Random Variables 42:08
Week 8 - Lecture 2 Expectation and the Cumulative Distribution Function 32:14
Week 8 - Lecture 3 Expectation and the Cumulative Distribution Function 56:38
Week 9 - Lecture 1 The Gaussian CDF 49:32
Week 9 - Lecture 2 Conditional PDFs, Joint PDFs 54:39
Week 9 - Lecture 3 Conditional PDFs, Joint PDFs 34:12
Week 10 - Lecture 1 Conditioning one random variable on another 53:03
Week 10 - Lecture 2 Independence, Continuous Bayes's Rule; Derived Distributions 38:58
Week 10 - Lecture 3 Independence, Continuous Bayes's Rule; Derived Distributions 52:25
Week 11 - Lecture 1 Derived Distributions 43:29
Week 11 - Lecture 2 Functions of Two Random Variables; Correlation and Covariance 43:48
Week 11 - Lecture 3 Functions of Two Random Variables; Correlation and Covariance 46:35
Week 12 - Lecture 1 Applications of Covariance 47:46
Week 12 - Lecture 2 Transforms (Moment Generating Functions) 49:02
Week 12 - Lecture 3 Transforms (Moment Generating Functions) 25:51
Week 13 - Lecture 1 Markov and Chebychev Inequalities, Convergence In Probability 33:38
Week 13 - Lecture 2 The Weak Law of Large Numbers 58:15
Week 13 - Lecture 3 [Part 1] The Central Limit Theorem 18:43
Week 13 - Lecture 3 [Part 2] The Central Limit Theorem 13:59
Week 14 - Lecture 1 The Bernoulli Process 48:42
Week 14 - Lecture 2 The Poisson Process 44:38
Week 14 - Lecture 3 The Poisson Process 39:20