`ChapterTotalVariance.total_variance` [Finite κ] (w : Ω → ℝ) (X : Ω → κ) (Y : Ω → ℝ) (hw : ∀ ω, 0 ≤ w ω) : variance w Y = within w X Y + between w X Y
ProvedChapterTotalVariance.total_variancetheoremstimepiece
Prove the following Lean 4 theorem from ChapterTotalVariance.
ChapterTotalVariance.total_variance [Finite κ] (w : Ω → ℝ) (X : Ω → κ) (Y : Ω → ℝ) (hw : ∀ ω, 0 ≤ w ω) : variance w Y = within w X Y + between w X Y
Formalization note: Lean 4 identifier ChapterTotalVariance.total_variance.
Preamble
-- Generated from ChapterTotalVariance.lean — theorem ChapterTotalVariance.total_variance
import Mathlib
import Definitions.Def_ChapterTotalVariance
import Definitions.Def_ChapterA4
open ChapterTotalVariance
open scoped BigOperators
open Finset
variable {Ω κ : Type*} [Fintype Ω] [DecidableEq κ]Formal statement
theorem ChapterTotalVariance.total_variance [Finite κ] (w : Ω → ℝ) (X : Ω → κ) (Y : Ω → ℝ)
(hw : ∀ ω, 0 ≤ w ω) :
variance w Y = within w X Y + between w X Y := by sorry