Theorems · Theorem · probability
ProbabilityTheory.IndepFun.variance_add
∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {X Y : Ω → ℝ},
MeasureTheory.MemLp X 2 μ →
MeasureTheory.MemLp Y 2 μ →
ProbabilityTheory.IndepFun X Y μ →
ProbabilityTheory.variance (X + Y) μ = ProbabilityTheory.variance X μ + ProbabilityTheory.variance Y μThe variance of the sum of two independent random variables is the sum of the variances.
- Defined in
- Mathlib.Probability.Moments.Variance
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 272 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- MeasureTheory.aeproof · cited by 2,352
- MulZeroClass.mul_zeroproof · cited by 2,091
- Filter.EventuallyEqproof · cited by 1,912
- MeasureTheory.MemLpstatement and proof · cited by 457
- MeasureTheory.IsProbabilityMeasureproof · cited by 392
- ProbabilityTheory.IndepFunstatement and proof · cited by 192
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.IndepFun.variance_fun_addproof · cited by 1
- ProbabilityTheory.IndepFun.hasGaussianLaw_sub_of_subproof · cited by 1