How to do CS Theory || @ CMU || Lecture 1b of CS Theory Toolkit
35:51Street Fighting Mathematics || @ CMU || Lecture 1c of TCS Toolkit
26:10Big O and friends || @ CMU || Lecture 2a of CS Theory Toolkit
28:10Harmonic Numbers Asymptotics || @ CMU || Lecture 2b of CS Theory Toolkit
22:18Asymptotics Tricks || @ CMU || Lecture 2c of CS Theory Toolkit
25:00The Central Binomial Coefficient || @ CMU || Recitation 1 of CS Theory Toolkit
1:00:26Birthday Paradox Asymptotics || @ CMU || Lecture 3a of CS Theory Toolkit
18:09Lecture 3b: Factorial Asymptotics, Stirling's Formula (15-750)
28:26Lecture 3c: Binomial Coefficients Asymptotics (15-750)
35:57Lecture 4a: Central Limit Theorem (15-750)
24:22Lecture 4b: Gaussian Random Variables (15-750)
38:31Lecture 4c: Berry --Esseen Theorem (15-750)
16:07Lecture 5a: Markov and Chebyshev Inequalities (15-750)
38:22Lecture 5b: Proof of the Chernoff Bound (15-750)
24:34Lecture 5c: Chernoff, Hoeffding, etc. bounds (15-750)
17:47Lecture 6a: Computational Models: Turing Machines (15-750)
25:31Lecture 6b: Computational Models: Circuits (15-750)
29:07Lecture 6c: The Word RAM Model (15-750)
25:30Lecture 4b: Gaussian Random Variables (15-750)
This lecture investigates the fundamental properties of Gaussian random variables, elucidating 'The Fact' from which many of their characteristics are derived.
Properties of Gaussian random variables, including The Fact from which most of these properties derive. Lecture 4b of "CS Theory Toolkit": a semester-long graduate course on math and CS fundamentals for research in theoretical computer science, taught at Carnegie Mellon University.
Resources for this lecture:
Feller's book, "Introduction to probability theory and its applications"
Lecture 4a: Central Limit Theorem (15-750)
Next · Lecture 12Lecture 4c: Berry --Esseen Theorem (15-750)