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

Averages
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.
https://en.wikipedia.org/wiki/Pythagorean_means

Seonglae Cho