Theorems · Theorem · probability
ProbabilityTheory.mgf_fun_id_gaussianReal
∀ {μ : ℝ} {v : NNReal},
ProbabilityTheory.mgf (fun x => x) (ProbabilityTheory.gaussianReal μ v) = fun t => Real.exp (μ * t + ↑v * t ^ 2 / 2)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 295 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 and proof · cited by 1,260
- Real.expstatement and proof · cited by 871
- ProbabilityTheory.mgfstatement · cited by 113
- ProbabilityTheory.gaussianRealstatement and proof · cited by 77
- MeasureTheory.Measure.map_id'proof · cited by 12
- ProbabilityTheory.mgf_gaussianRealproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- ProbabilityTheory.integral_id_gaussianRealproof · cited by 6
- ProbabilityTheory.variance_fun_id_gaussianRealproof · cited by 1
- ProbabilityTheory.mgf_id_gaussianRealproof · cited by 0