Theory of probability distributions | Independence (probability theory)
In probability theory, a pairwise independent collection of random variables is a set of random variables any two of which are independent. Any collection of mutually independent random variables is pairwise independent, but some pairwise independent collections are not mutually independent. Pairwise independent random variables with finite variance are uncorrelated. A pair of random variables X and Y are independent if and only if the random vector (X, Y) with joint cumulative distribution function (CDF) satisfies or equivalently, their joint density satisfies That is, the joint distribution is equal to the product of the marginal distributions. Unless it is not clear in context, in practice the modifier "mutual" is usually dropped so that independence means mutual independence. A statement such as " X, Y, Z are independent random variables" means that X, Y, Z are mutually independent. (Wikipedia).
(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
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From playlist A Second Course in Differential Equations
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From playlist Probability Theory
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This video introduced the topic of linearly independent and dependent sets of vectors.
From playlist Linear Independence and Bases
Differential Equations: Linear Independence
Linear independence is a core idea from Linear Algebra. Surprisingly, it's also important in differential equations. This video is the second precursor to our discussion of homogeneous differential equations.
From playlist Differential Equations
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In this video, I work through several practice problems relating to the concept of linear independence. These including using the definition of linear independence, as well as "shortcuts" to determine whether a set is linearly independent without solving a vector equation.
From playlist Linear Algebra Lectures
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(PP 5.4) Independence, Covariance, and Correlation
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From playlist Probability Theory
STAT 200 Lesson 10 Video Lecture
Table of Contents: 00:00 - Introduction 00:35 - Learning Objectives 01:02 - 1. Explain why it is not appropriate to conduct multiple independent t tests to compare the means of more than two independent groups 04:32 - 2. Use Minitab to construct a probability plot for an F distribution
From playlist STAT 200 Video Lectures
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From playlist MIT 6.042J Mathematics for Computer Science, Spring 2015
On the Approximation Resistance of Balanced Linear Threshold Functions - Aaron Potechin
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From playlist MIT RES.6-012 Introduction to Probability, Spring 2018
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From playlist Factorial ANOVA
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4.4.2 Random Variables: Independence: Video
MIT 6.042J Mathematics for Computer Science, Spring 2015 View the complete course: http://ocw.mit.edu/6-042JS15 Instructor: Albert R. Meyer License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.042J Mathematics for Computer Science, Spring 2015
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ANOVA 5: Factorial / Two-Way ANOVA using GLM
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From playlist Factorial ANOVA