IV111 Probability in Computer Science
Lectures -- video materials from fall 2020
Lecture 1 -- Introduction and Basic Definitions
October 9, 2020
Videos:
Lecture 2 -- Random Variables
October 16, 2020
Videos:
- Lect 02 Part 1 -- Review
- Lect 02 Part 2 -- Random Variables
- Lect 02 Part 3 -- Examples of Probability Distributions
- Lect 02 Part 4 -- Continuous Random Variables
- Lect 02 Part 5 -- Discrete Random Vectors
- Lect 02 Part 6 & 7 -- Independent Random Variables & Functions of Random Variables
Lecture 3 -- Expectation and Markov Inequality
October 23, 2020
Videos:
- Lect 03 Part 0 -- Review
- Lect 03 Part 1 -- Expectation of Random Variables
- Lect 03 Part 2 -- Functions of Random Variables
- Lect 03 Part 3 -- Markov Inequality
- Lect 03 Part 4 -- Moments and Deviations
Lecture 4 -- Variance and Chebyshev Inequality
October 30, 2020
Videos:
- Lect 04 Part 1 -- Review
- Lect 04 Part 2 -- Moments and Deviations
- Lect 04 Part 3 -- Conditional Distribution and Expectation
- Lect 04 Part 4 -- Chebyshev Inequality
Lecture 5 -- Chernoff Bounds and Laws of Large Numbers
November 6, 2020
Videos:
- Lect 05 Part 1 -- Motivation Examples
- Lect 05 Part 2 -- Moment Generating Function
- Lect 05 Part 3 -- Chernoff Bounds
- Lect 05 Part 4 -- Laws of Large Numbers
Lecture 6 -- Stochastic Processes and Markov Chains
November 13, 2020
Videos:
- Lect 06 Part 1 -- Stochastic Processes
- Lect 06 Part 2 -- Markov Chains
- Lect 06 Part 3 -- Reachability and Hitting Time
Lecture 7 -- Long-Run Analysis of DTMC
November 20, 2020
Videos:
- Lect 07 Part 1 -- Revision
- Lect 07 Part 2 -- Long-Run Analysis
- Lect 07 Part 3 -- Infinite-State Markov Chains
Lecture 8 -- Continuous-Time Markov Chains
November 27, 2020
Videos:
- Lect 08 Part 1 -- Motivation and Memoryless Distr
- Lect 08 Part 2 -- CTMC
- Lect 08 Part 3 -- Queues as examples of CTMC
- Lect 08 Part 4 -- CTMC Analysis
- Lect 08 Part 5 -- Tools and Non-Markov Models
Lecture 9 -- Information Theory
December 4, 2020
Videos:
- Lect 09 Part 1 -- Uncertainty and Entropy
- Lect 09 Part 2 -- Joint and Conditional Entropy
- Lect 09 Part 3 -- Cross-Entropy, Relative Entropy, and Mutual Information
- Lect 09 Part 4 -- Properties of Entropy and Mutual Information
- Lect 09 Part 5 -- Information inequalities
Lecture 10 -- Codes for Data Compression
December 11, 2020
Videos:
- Lect 10 Part 1 -- Optimal Length of Code
- Lect 10 Part 2 -- Kraft Inequality
- Lect 10 Part 3 -- McMillan Inequality
- Lect 10 Part 4 -- Optimal Codes
Lecture 11-- Optimal Codes
December 18, 2020
Videos:
- Lect 11 Part 1 -- Revision
- Lect 11 Part 2 -- Shannon-Fano Coding and Bounds on the Optimal Code Length
- Lect 11 Part 3 -- Shannon-Fano and Huffman Codes
- Lect 11 Part 4 -- Proof of Optimality
- Lect 11 Part 5 -- Data Compression in Practice
- Lect 11 Part 6 -- Generating Discrete Distribution Using Fair-Coin Tosses
Lecture 12 -- Channel Capacity
January 8, 2021
Videos: