Articles containing proofs | Theory of probability distributions | Statistical laws | Algebra of random variables | Statistical deviation and dispersion | Theorems in statistics

Law of total variance

In probability theory, the law of total variance or variance decomposition formula or conditional variance formulas or law of iterated variances also known as Eve's law, states that if and are random variables on the same probability space, and the variance of is finite, then In language perhaps better known to statisticians than to probability theorists, the two terms are the "unexplained" and the "explained" components of the variance respectively (cf. fraction of variance unexplained, explained variation). In actuarial science, specifically credibility theory, the first component is called the expected value of the process variance (EVPV) and the second is called the variance of the hypothetical means (VHM). These two components are also the source of the term "Eve's law", from the initials EV VE for "expectation of variance" and "variance of expectation". (Wikipedia).

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Variance (4 of 4: Proof of two formulas)

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From playlist Random Variables

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CLT.4.Variance of Sample Means

This video is brought to you by the Quantitative Analysis Institute at Wellesley College. The material is best viewed as part of the online resources that organize the content and include questions for checking understanding: https://www.wellesley.edu/qai/onlineresources

From playlist Central Limit Theorem

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How to find the number of standard deviations that it takes to represent all the data

👉 Learn how to find the variance and standard deviation of a set of data. The variance of a set of data is a measure of spread/variation which measures how far a set of numbers is spread out from their average value. The standard deviation of a set of data is a measure of spread/variation

From playlist Variance and Standard Deviation

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How to find the variance and standard deviation from a set of data

👉 Learn how to find the variance and standard deviation of a set of data. The variance of a set of data is a measure of spread/variation which measures how far a set of numbers is spread out from their average value. The standard deviation of a set of data is a measure of spread/variation

From playlist Variance and Standard Deviation

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MIT RES.6-012 Introduction to Probability, Spring 2018 View the complete course: https://ocw.mit.edu/RES-6-012S18 Instructor: John Tsitsiklis License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu

From playlist MIT RES.6-012 Introduction to Probability, Spring 2018

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More Standard Deviation and Variance

Further explanations and examples of standard deviation and variance

From playlist Unit 1: Descriptive Statistics

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From playlist Variance and Standard Deviation

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Covariance (1 of 17) What is Covariance? in Relation to Variance and Correlation

Visit http://ilectureonline.com for more math and science lectures! To donate:a http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn the difference between the variance and the covariance. A variance (s^2) is a measure of how spread out the numbers of

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L13.9 Section Means and Variances

MIT RES.6-012 Introduction to Probability, Spring 2018 View the complete course: https://ocw.mit.edu/RES-6-012S18 Instructor: John Tsitsiklis License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu

From playlist MIT RES.6-012 Introduction to Probability, Spring 2018

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A Coin with Random Bias

MIT 6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013 View the complete course: http://ocw.mit.edu/6-041SCF13 Instructor: Jimmy Li 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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MIT RES.6-012 Introduction to Probability, Spring 2018 View the complete course: https://ocw.mit.edu/RES-6-012S18 Instructor: John Tsitsiklis License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu

From playlist MIT RES.6-012 Introduction to Probability, Spring 2018

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Widgets and Crates

MIT 6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013 View the complete course: http://ocw.mit.edu/6-041SCF13 Instructor: Jimmy Li 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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12. Iterated Expectations

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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Limiting Laws in Some Subsequences Problems by Christian Houdré

PROGRAM : FIRST-PASSAGE PERCOLATION AND RELATED MODELS (HYBRID) ORGANIZERS : Riddhipratim Basu (ICTS-TIFR, India), Jack Hanson (City University of New York, US) and Arjun Krishnan (University of Rochester, US) DATE : 11 July 2022 to 29 July 2022 VENUE : Ramanujan Lecture Hall and online T

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L13.8 A Simple Example

MIT RES.6-012 Introduction to Probability, Spring 2018 View the complete course: https://ocw.mit.edu/RES-6-012S18 Instructor: John Tsitsiklis License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu

From playlist MIT RES.6-012 Introduction to Probability, Spring 2018

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Introduction to Probability and Statistics 131B. Lecture 05.

UCI Math 131B: Introduction to Probability and Statistics (Summer 2013) Lec 05. Introduction to Probability and Statistics View the complete course: http://ocw.uci.edu/courses/math_131b_introduction_to_probability_and_statistics.html Instructor: Michael C. Cranston, Ph.D. License: Creativ

From playlist Introduction to Probability and Statistics 131B

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(PP 4.5) Mean, variance, and moments

Definitions of mean, variance, and moments. A playlist of the Probability Primer series is available here: http://www.youtube.com/view_play_list?p=17567A1A3F5DB5E4

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Davar Khoshnevisan (Utah) -- Ergodicity and CLT for SPDEs

I will summarize some of the recent collaborative work with Le Chen, David Nualart, and Fei Pu in which we characterize when the solution to a large family of parabolic stochastic PDE is ergodic in its spatial variable. We also identify when there are Gaussian fluctuations associated to th

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Variance | Random variable | Fraction of variance unexplained | Correlation | Law of total cumulance | Probability theory | Credibility theory | Mutual information | Explained variation | Actuarial science | Central moment | Probability space | Natural filtration | Cumulant | Conditional variance | Law of total expectation