The algebra of random variables in statistics, provides rules for the symbolic manipulation of random variables, while avoiding delving too deeply into the mathematically sophisticated ideas of probability theory. Its symbolism allows the treatment of sums, products, ratios and general functions of random variables, as well as dealing with operations such as finding the probability distributions and the expectations (or expected values), variances and covariances of such combinations. In principle, the elementary algebra of random variables is equivalent to that of conventional non-random (or deterministic) variables. However, the changes occurring on the probability distribution of a random variable obtained after performing algebraic operations are not straightforward. Therefore, the behavior of the different operators of the probability distribution, such as expected values, variances, covariances, and moments, may be different from that observed for the random variable using symbolic algebra. It is possible to identify some key rules for each of those operators, resulting in different types of algebra for random variables, apart from the elementary symbolic algebra: Expectation algebra, Variance algebra, Covariance algebra, Moment algebra, etc. (Wikipedia).
Algebra for Beginners | Basics of Algebra
#Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. Table of Conten
From playlist Linear Algebra
(PP 3.1) Random Variables - Definition and CDF
(0:00) Intuitive examples. (1:25) Definition of a random variable. (6:10) CDF of a random variable. (8:28) Distribution of a random variable. A playlist of the Probability Primer series is available here: http://www.youtube.com/view_play_list?p=17567A1A3F5DB5E4
From playlist Probability Theory
Algebra for beginners || Basics of Algebra
In this course you will learn about algebra which is ideal for absolute beginners. #Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. It involves variables like x, y, z, and mathematical operations like
From playlist Algebra
10A An Introduction to Eigenvalues and Eigenvectors
A short description of eigenvalues and eigenvectors.
From playlist Linear Algebra
Linear Algebra: Continuing with function properties of linear transformations, we recall the definition of an onto function and give a rule for onto linear transformations.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
(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
Linear Algebra - Lecture 33 - Eigenvectors and Eigenvalues
In this lecture, we define eigenvectors and eigenvalues of a square matrix. We also prove a couple of useful theorems related to these concepts.
From playlist Linear Algebra Lectures
Determining if a vector is a linear combination of other vectors
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Determining if a vector is a linear combination of other vectors
From playlist Linear Algebra
Camille Male - Distributional symmetry of random matrices...
Camille Male - Distributional symmetry of random matrices and the non commutative notions of independence
From playlist Spectral properties of large random objects - Summer school 2017
4. Forbidding a subgraph III: algebraic constructions
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX How does one construct graphs that do not contain complet
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
(PP 3.4) Random Variables with Densities
(0:00) Probability density function (PDF). (3:20) Indicator functions. (5:00) Examples of random variables with densities: Uniform, Exponential, Beta, Normal/Gaussian. A playlist of the Probability Primer series is available here: http://www.youtube.com/view_play_list?p=17567A1A3F5
From playlist Probability Theory
Probability Theory - Part 10 - Random Variables [dark version]
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From playlist Probability Theory [dark version]
Random Matrices and Their Limits - R. Speicher - Workshop 2 - CEB T3 2017
Roland Speicher / 26.10.17 Random Matrices and Their Limits The free probability perspective on random matrices is that the large size limit of random matrices is given by some (usually interesting) operators on Hilbert spaces and corresponding operator algebras. The prototypical example
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
John Terilla : A collection of Homotopy Random Variables
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 29, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Geometry
Piotr Sniady: Representation theory from the random matrix perspective
Talk at the conference "Noncommutative geometry meets topological recursion", August 2021, University of Münster. Abstract: In many cases a representation of a group can be viewed as a "random matrix with non-commutative entries". This viewpoint gives a heuristic explanation for many links
From playlist Noncommutative geometry meets topological recursion 2021
Anna Seigal: "Tensors in Statistics and Data Analysis"
Watch part 1/2 here: https://youtu.be/9unKtBoO5Hw Tensor Methods and Emerging Applications to the Physical and Data Sciences Tutorials 2021 "Tensors in Statistics and Data Analysis" Anna Seigal - University of Oxford Abstract: I will give an overview of tensors as they arise in settings
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
9A_4 The Inverse of a Matrix Using the Determinant
Calculating the inverse of a matrix by use of the determinant of the matrix
From playlist Linear Algebra