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Probability for Computer Science

Probability for Computer Science. Instructor: Prof. Nitin Saxena, Department of Computer Science and Engineering, IIT Kanpur. Probability is one of the most important ideas in human knowledge. This is a crash course to introduce the concept of probability formally; and exhibit its applications in computer science, combinatorics, and algorithms. The course will be different from a typical mathematics course in the coverage and focus of examples. After finishing this course a student will have a good understanding of both theory and practice of probability in diverse areas. (from nptel.ac.in)

Lecture 12 - Continuous Random Variables


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Lecture 01 - Introductory Examples
Lecture 02 - Examples and Course Outline
Lecture 03 - Probability over Discrete Space
Lecture 04 - Inclusion-Exclusion Principle
Lecture 05 - Probability over Infinite Space
Lecture 06 - Conditional Probability, Partition Formula
Lecture 07 - Independent Events, Bayes Theorem
Lecture 08 - Fallacies, Random Variables
Lecture 09 - Expectation
Lecture 10 - Conditional Expectation
Lecture 11 - Important Random Variables
Lecture 12 - Continuous Random Variables
Lecture 13 - Equality Checking, Poisson Distribution
Lecture 14 - Concentration Inequalities, Variance
Lecture 15 - Weak Linearity of Variance, Law of Large Numbers
Lecture 16 - Chernoff's Bound, K-wise Independence
Lecture 17 - Union and Factorial Estimates
Lecture 18 - Stochastic Process: Markov Chains
Lecture 19 - Drunkard's Walk, Evolution of Markov Chains
Lecture 20 - Stationary Distribution
Lecture 21 - Ferron-Frobenius Theorem, PageRank Algorithm
Lecture 22 - PageRank Algorithm: Ergodicity
Lecture 23 - Cell Genetics
Lecture 24 - Random Sampling
Lecture 25 - Biased Coin Tosses, Hashing
Lecture 26 - Hashing, Introduction to Probabilistic Methods
Lecture 27 - Ramsey Numbers, Large Cuts in Graphs
Lecture 28 - Sum Free Subsets, Discrepancy
Lecture 29 - Extremal Set Families
Lecture 30 - Super Concentrators
Lecture 31 - Streaming Algorithms I
Lecture 32 - Streaming Algorithms II