(PP 6.1) Multivariate Gaussian - definition
Introduction to the multivariate Gaussian (or multivariate Normal) distribution.
From playlist Probability Theory
Uniform Probability Distribution Examples
Overview and definition of a uniform probability distribution. Worked examples of how to find probabilities.
From playlist Probability Distributions
(PP 6.6) Geometric intuition for the multivariate Gaussian (part 1)
How to visualize the effect of the eigenvalues (scaling), eigenvectors (rotation), and mean vector (shift) on the density of a multivariate Gaussian.
From playlist Probability Theory
(PP 6.2) Multivariate Gaussian - examples and independence
Degenerate multivariate Gaussians. Some sketches of examples and non-examples of Gaussians. The components of a Gaussian are independent if and only if they are uncorrelated.
From playlist Probability Theory
(PP 6.7) Geometric intuition for the multivariate Gaussian (part 2)
How to visualize the effect of the eigenvalues (scaling), eigenvectors (rotation), and mean vector (shift) on the density of a multivariate Gaussian.
From playlist Probability Theory
Central Limit Theorem: Verification using Uniform Distribution with samples in the range of 0 and 10
This script is to verify the Central Limit Theorem in probability theory or statistics. The Central Limit Theorem states that, regardless of the distribution of the population, the sampling distribution of the sample means, assuming all samples are identical in size, will approach a norma
From playlist Probability Theory/Statistics
(PP 6.3) Gaussian coordinates does not imply (multivariate) Gaussian
An example illustrating the fact that a vector of Gaussian random variables is not necessarily (multivariate) Gaussian.
From playlist Probability Theory
(PP 2.3) Independence (continued)
(0:00) (Mutual) Independence of an infinite sequence of events. (1:55) Conditional Independence of multiple events. (3:28) Relationship between independence and conditional probability. (7:23) Example illustrating the relationships between independence, pairwise independence, mutu
From playlist Probability Theory
10. The Universe and Three Examples | MIT 8.224 Exploring Black Holes
Lecturer: Alan Guth View the complete course at: http://ocw.mit.edu/8-224S03 *NOTE: Sessions 11, 12 have no video. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT Exploring Black Holes: General Relativity & Astrophysics
Gregory Margulis - The Abel Prize interview 2020
00:00 congratulations to Gregory Margulis 01:33 when did you interests in mathematics start? 02:33 growing up in Moscow in the 50’s and 60’s and being included in mathematical circles 05:47 mathematical Olympiads 06:32 early career and the paper with Kazhdan 08:03 Margulis at the Institute
From playlist Gregory Margulis
UNIFORM Probability Distribution for Discrete Random Variables (9-5)
Uniform Probability Distribution: (i.e., a rectangular distribution) is a probability distribution involving one random variable with a constant probability. Each potential outcome is equally likely, such as flipping coin and getting heads is always 50/50. On Chaos Night, Dante experiment
From playlist Discrete Probability Distributions in Statistics (WK 9 - QBA 237)
Structure vs Randomness in Complexity Theory - Rahul Santhanam
Computer Science/Discrete Mathematics Seminar I Topic: Structure vs Randomness in Complexity Theory Speaker: Rahul Santhanam Affiliation: University of Oxford Date: April 20, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Looking into the future of high-energy particle physics (Lecture 3) by Gian Giudice
INFOSYS-ICTS CHANDRASEKHAR LECTURES LOOKING INTO THE FUTURE OF HIGH-ENERGY PARTICLE PHYSICS SPEAKER: Gian Giudice (CERN, Switzerland) DATE : 23 November 2022, 17:00 to 18:00 VENUE: Ramanujan Lecture Hall Title: Looking into the future of high-energy particle physics Abstract: P
From playlist Infosys-ICTS Chandrasekhar Lectures
Root Finding and Broadcasting in Random Recursive Trees by Gabor Lugosi
Program Advances in Applied Probability II (ONLINE) ORGANIZERS: Vivek S Borkar (IIT Bombay, India), Sandeep Juneja (TIFR Mumbai, India), Kavita Ramanan (Brown University, Rhode Island), Devavrat Shah (MIT, US) and Piyush Srivastava (TIFR Mumbai, India) DATE: 04 January 2021 to 08 Januar
From playlist Advances in Applied Probability II (Online)
The Abel lectures: Hillel Furstenberg and Gregory Margulis
0:30 Welcome by Hans Petter Graver, President of the Norwegian Academy of Science Letters 01:37 Introduction by Hans Munthe-Kaas, Chair of the Abel Prize Committee 04:16 Hillel Furstenberg: Random walks in non-euclidean space and the Poisson boundary of a group 58:40 Questions and answers
From playlist Gregory Margulis
Random orderings and unique ergodicity of automorphism groups - Russell Lyons
Conference on Graphs and Analysis Russell Lyons June 4, 2012 More videos on http://video.ias.edu
From playlist Mathematics
WSU Master Class: Inflationary Cosmology with Alan Guth
Breakthrough Prize winner Alan Guth developed the theory of inflation to answer to our cosmic origins. It's one of the most studied and debated theories in cosmology, with research propelling Guth’s work to the forefront of scientific conversation. In this Master Class, Professor Guth add
From playlist WSU Master Class
Antonio Rieser (03/29/23) Algebraic Topology for Graphs & Mesoscopic Spaces: Homotopy & Sheaf Theory
Title: Algebraic Topology for Graphs and Mesoscopic Spaces: Homotopy and Sheaf Theory Abstract: In this talk, we introduce the notion of a mesoscopic space: a metric space decorated with a privileged scale, and we survey recent developments in the algebraic topology of such spaces. Our ap
From playlist AATRN 2023
The Law of Total Probability | Probability Theory, Total Probability Rule
What is the law of total probability? Also sometimes called the total probability rule, we go over this tremendously useful law in today’s full video math lesson! Imagine we have a sample space that can be partitioned into three events B1, B2, and B3. And say we have another event in this
From playlist Probability Theory
From playlist Plenary talks One World Symposium 2020