Theorems · Theorem · probability
ProbabilityTheory.variance_fun_id_gaussianReal
∀ {μ : ℝ} {v : NNReal}, ProbabilityTheory.variance (fun x => x) (ProbabilityTheory.gaussianReal μ v) = ↑vThe variance of a real Gaussian distribution gaussianReal μ v is
its variance parameter v.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 299 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites48
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
- NNRealstatement and proof · cited by 4,310
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- MulZeroClass.mul_zeroproof · cited by 2,091
- MeasureTheory.integralproof · cited by 1,779
- MulZeroClass.zero_mulproof · cited by 1,625
- NNReal.toRealstatement and proof · cited by 1,260
- sub_selfproof · cited by 996
- pow_oneproof · cited by 894
- Real.expproof · cited by 871
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.variance_id_gaussianRealproof · cited by 4