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Expectation value

Creator
Creator
Seonglae ChoSeonglae Cho
Created
Created
2023 Mar 9 1:27
Editor
Editor
Seonglae ChoSeonglae Cho
Edited
Edited
2025 Jan 29 23:12
Refs
Refs

Average, Mean

Expectation operator is linear

k-th moment of X

defined as the expected value of x raised to the power of k
If only X, Y is independence,
 
does not means
Expectation value Notion
Law of total expectation
The law of Large number
 
 
 
notion image
Averages
Arithmetic Mean
Geometric Average
Polyak average
Harmonic Mean
 
 
 
 
Harmonic Mean
,
Arithmetic Mean
and
Harmonic Mean
are Pythagorean means
Pythagorean means
In mathematics, the three classical Pythagorean means are the arithmetic mean (AM), the geometric mean (GM), and the harmonic mean (HM). These means were studied with proportions by Pythagoreans and later generations of Greek mathematicians because of their importance in geometry and music.
Pythagorean means
https://en.wikipedia.org/wiki/Pythagorean_means
Pythagorean means
 
 

Table of Contents
Average, MeanExpectation operator is lineark-th moment of X

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Expectation value
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