Theorems · Theorem · probability
ProbabilityTheory.variance_id_gaussianReal
∀ {μ : ℝ} {v : NNReal}, ProbabilityTheory.variance id (ProbabilityTheory.gaussianReal μ v) = ↑vThe variance of a real Gaussian distribution gaussianReal μ v is
its variance parameter v.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 300 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- NNReal.toRealstatement · cited by 1,260
- ProbabilityTheory.variancestatement · cited by 104
- ProbabilityTheory.gaussianRealstatement · cited by 77
- ProbabilityTheory.variance_fun_id_gaussianRealproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- ProbabilityTheory.HasIndepIncrements.isPreBrownianReal_of_hasLawproof · cited by 1
- ProbabilityTheory.variance_linearMap_gaussianRealproof · cited by 1
- ProbabilityTheory.variance_dual_stdGaussianproof · cited by 1
- ProbabilityTheory.gaussianReal_ext_iffproof · cited by 0