Theorems · Theorem · probability
ProbabilityTheory.binomial_eq_sum_dirac
∀ (n : ℕ) (p : ↑unitInterval),
ProbabilityTheory.binomial n p =
∑ k ≤ n, ENNReal.ofReal (↑(n.choose k) * ↑p ^ k * (1 - ↑p) ^ (n - k)) • MeasureTheory.Measure.dirac k- Cited by
- 2 results in Mathlib
- Foundations
- Depth 292 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- MeasureTheory.Measurestatement · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Set.Elemstatement and proof · cited by 7,166
- Finset.sumstatement and proof · cited by 5,195
- mul_oneproof · cited by 3,885
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- ENNReal.ofRealstatement and proof · cited by 863
- zero_smulproof · cited by 716
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.map_cast_binomial_eq_sum_diracproof · cited by 1
- ProbabilityTheory.integral_binomialproof · cited by 1