Editing Law of total variance (section)

== Explanation ==
Let {{mvar|Y}} be a random variable and {{mvar|X}} another random variable on the same probability space. The law of total variance can be understood by noting:

# <math>\operatorname{Var}(Y \mid X)</math> measures how much {{mvar|Y}} varies around its conditional mean <math>\operatorname{E}[Y\mid X].</math>
# Taking the expectation of this conditional variance across all values of {{mvar|X}} gives <math>\operatorname{E}[\operatorname{Var}(Y \mid X)]</math>, often termed the “unexplained” or within-group part.
# The variance of the conditional mean, <math>\operatorname{Var}(\operatorname{E}[Y\mid X])</math>, measures how much these conditional means differ (i.e. the “explained” or between-group part).

Adding these components yields the total variance <math>\operatorname{Var}(Y)</math>, mirroring how [[analysis of variance]] partitions variation.