Measure theory | Experiment (probability theory)
In probability theory, a standard probability space, also called Lebesgue–Rokhlin probability space or just Lebesgue space (the latter term is ambiguous) is a probability space satisfying certain assumptions introduced by Vladimir Rokhlin in 1940. Informally, it is a probability space consisting of an interval and/or a finite or countable number of atoms. The theory of standard probability spaces was started by von Neumann in 1932 and shaped by Vladimir Rokhlin in 1940. Rokhlin showed that the unit interval endowed with the Lebesgue measure has important advantages over general probability spaces, yet can be effectively substituted for many of these in probability theory. The dimension of the unit interval is not an obstacle, as was clear already to Norbert Wiener. He constructed the Wiener process (also called Brownian motion) in the form of a measurable map from the unit interval to the space of continuous functions. (Wikipedia).
(PP 6.1) Multivariate Gaussian - definition
Introduction to the multivariate Gaussian (or multivariate Normal) distribution.
From playlist Probability Theory
Random variables, means, variance and standard deviations | Probability and Statistics
We introduce the idea of a random variable X: a function on a probability space. Associated to such a function is something called a probability distribution, which assigns probabilities, say p_1,p_2,...,p_n to the various possible values of X, say x_1,x_2,...,x_n. The probabilities p_i h
From playlist Probability and Statistics: an introduction
(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 5.1) Multiple discrete random variables
(0:00) Definition of a random vector. (1:50) Definition of a discrete random vector. (2:28) Definition of the joint PMF of a discrete random vector. (7:00) Functions of random vectors. A playlist of the Probability Primer series is available here: http://www.youtube.com/view_play_list?p=
From playlist Probability Theory
The normal distribution | Probability and Statistics | NJ Wildberger
In this final lecture in this short introduction to Probability and Statistics, we introduce perhaps the most important probability distibution: the normal distribution, also known as the `bell-curve'. Its role is clarified by the Central Limit theorem, a key result in Statistics, that sta
From playlist Probability and Statistics: an introduction
Probabiilty spaces, events and conditional probabilities | Probability and Statistics
We now introduce some more formal structures to talk about probabillities: first the idea of a sample space S--the possible outcomes of an experiment, and then the idea of a probability measure P on such a sample space. Together these two (S,P) make what we call a probability space. An e
From playlist Probability and Statistics: an introduction
(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
Matrix liberation process - Y. Ueda - Workshop 2 - CEB T3 2017
Yoshimichi Ueda / 24.10.17 Matrix liberation process We introduce a natural random matrix counterpart of the so-called liberation process introduced by Voiculescu in the framework of free probability, and consider its possible LDP in the large N limit. ---------------------------------
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Probability notation and terms, When you have equally likely outcomes, Conditional probability
Probability notation and terms, When you have equally likely outcomes, Conditional probability
From playlist Exam 1 material
Semantic models for higher-order Bayesian inference - Sam Staton, University of Oxford
In this talk I will discuss probabilistic programming as a method of Bayesian modelling and inference, with a focus on fully featured probabilistic programming languages with higher order functions, soft constraints, and continuous distributions. These languages are pushing the limits of e
From playlist Logic and learning workshop
Types Of Distribution In Statistics | Probability Distribution Explained | Statistics | Simplilearn
🔥 Advanced Certificate Program In Data Science: https://www.simplilearn.com/pgp-data-science-certification-bootcamp-program?utm_campaign=TypesOfDistributionInStatistics&utm_medium=Descriptionff&utm_source=youtube 🔥 Data Science Bootcamp (US Only): https://www.simplilearn.com/data-science-b
From playlist Data Science Course | Simplilearn 🔥[2022 Updated]
Albert Cohen: Theory of approximation of hight-dimensional functions - lecture 2
Recorded during the meeting "Data Assimilation and Model Reduction in High Dimensional Problems" the July 20, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Luca Récanzone A kinetic description of a plasma in external and self-consistent fiel
From playlist Numerical Analysis and Scientific Computing
Self-Interacting Neutrinos: Unified Path to Dark Matter and Cosmological Tensions by Mansi Dhuria
PROGRAM LESS TRAVELLED PATH TO THE DARK UNIVERSE ORGANIZERS: Arka Banerjee (IISER Pune), Subinoy Das (IIA, Bangalore), Koushik Dutta (IISER, Kolkata), Raghavan Rangarajan (Ahmedabad University) and Vikram Rentala (IIT Bombay) DATE & TIME: 13 March 2023 to 24 March 2023 VENUE: Ramanujan
From playlist LESS TRAVELLED PATH TO THE DARK UNIVERSE
8. Continuous Random Variables
MIT 6.041 Probabilistic Systems Analysis and Applied Probability, Fall 2010 View the complete course: http://ocw.mit.edu/6-041F10 Instructor: John Tsitsiklis License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013
The 1-loop effective potential for the Standard (...) - T. Markkanen - Workshop 1 - CEB T3 2018
Tommi Markkanen (Imperial College London) / 18.09.2018 The 1-loop effective potential for the Standard Model in curved spacetime ---------------------------------- Vous pouvez nous rejoindre sur les réseaux sociaux pour suivre nos actualités. Facebook : https://www.facebook.com/Institut
From playlist 2018 - T3 - Analytics, Inference, and Computation in Cosmology
Prob & Stats - Random Variable & Prob Distribution (30 of 53) Standard Deviation
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the standard deviation of random variables. Next video in series: http://youtu.be/XiTMW8-aXXM
From playlist iLecturesOnline: Probability & Stats 2: Random Variable & Probability Distribution
Markus Haase : On some operator-theoretic aspects of ergodic theory
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Dynamical Systems and Ordinary Differential Equations
Karol Życzkowski : Geometry of Quantum Entanglement
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 31, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematician
From playlist Geometry
Brief overview of the standard error. What it represents and how you would find it with a formula.
From playlist Basic Statistics (Descriptive Statistics)