Theorems · Theorem · probability
ProbabilityTheory.variance_sub
∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {X Y : Ω → ℝ} {μ : MeasureTheory.Measure Ω} [MeasureTheory.IsFiniteMeasure μ],
MeasureTheory.MemLp X 2 μ →
MeasureTheory.MemLp Y 2 μ →
ProbabilityTheory.variance (X - Y) μ =
ProbabilityTheory.variance X μ - 2 * ProbabilityTheory.covariance X Y μ + ProbabilityTheory.variance Y μ- Defined in
- Mathlib.Probability.Moments.Variance
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 258 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- sub_eq_add_negproof · cited by 1,023
- MeasureTheory.MemLpstatement and proof · cited by 457
- ProbabilityTheory.variancestatement and proof · cited by 104
- ProbabilityTheory.covariancestatement and proof · cited by 96
- MeasureTheory.MemLp.negproof · cited by 12
- ProbabilityTheory.variance_addproof · cited by 5
- ProbabilityTheory.covariance_neg_rightproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.variance_fun_subproof · cited by 1