Law of total variance

Creator

Creator

Seonglae Cho

Created

Created

2023 Jul 13 8:42

Editor

Editor

Seonglae Cho

Edited

Edited

2024 Oct 22 11:26

Refs

Refs

Marginalization

Law of total expectation

Variance decomposition formula, conditional variance formulas or law of iterated variances also known as Eve's law

EVPV(expected value of the process variance) + VHM (variance of the hypothetical means)

X의 변화에 따른 Y의 평균 변동성 + X를 알고도 남는 Y의 불확실성

XY 2차원 분포 생각하면 이해 편하다 - E[], V[] 결과가 상수가 아니라 함수로 나옴 적분위해

decomposes the variance of two random variables on the same probability space into "explained" and "unexplained" components

Eve's law, from the initials EV VE for "expectation of variance" and "variance of expectation".

Law of total variance

In probability theory, the law of total variance[1] or variance decomposition formula or conditional variance formulas or law of iterated variances also known as Eve's law,[2] states that if X {\displaystyle X} and Y {\displaystyle Y} are random variables on the same probability space, and the variance of Y {\displaystyle Y} is finite, then

Law of total variance

https://en.wikipedia.org/wiki/Law_of_total_variance

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