Measure theory | Experiment (probability theory)

Standard probability space

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).

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(PP 6.1) Multivariate Gaussian - definition

Introduction to the multivariate Gaussian (or multivariate Normal) distribution.

From playlist Probability Theory

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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

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(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

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(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

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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

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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

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(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

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Matrix liberation process - Y. Ueda - Workshop 2 - CEB T3 2017

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From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester

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Probability notation and terms, When you have equally likely outcomes, Conditional probability

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From playlist Exam 1 material

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From playlist Logic and learning workshop

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From playlist Data Science Course | Simplilearn 🔥[2022 Updated]

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From playlist Numerical Analysis and Scientific Computing

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Self-Interacting Neutrinos: Unified Path to Dark Matter and Cosmological Tensions by Mansi Dhuria

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From playlist LESS TRAVELLED PATH TO THE DARK UNIVERSE

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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

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The 1-loop effective potential for the Standard (...) - T. Markkanen - Workshop 1 - CEB T3 2018

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From playlist 2018 - T3 - Analytics, Inference, and Computation in Cosmology

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From playlist iLecturesOnline: Probability & Stats 2: Random Variable & Probability Distribution

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Markus Haase : On some operator-theoretic aspects of ergodic theory

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From playlist Dynamical Systems and Ordinary Differential Equations

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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

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Intro to standard error

Brief overview of the standard error. What it represents and how you would find it with a formula.

From playlist Basic Statistics (Descriptive Statistics)

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