Theorems · Theorem · probability
ProbabilityTheory.binomial_real_singleton
∀ (n k : ℕ) (p : ↑unitInterval), (ProbabilityTheory.binomial n p).real {k} = ↑(n.choose k) * ↑p ^ k * (1 - ↑p) ^ (n - k)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 290 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- MeasureTheory.Measureproof · cited by 10,939
- Set.Elemstatement and proof · cited by 7,166
- unitIntervalstatement and proof · cited by 607
- MeasureTheory.Measure.realstatement and proof · cited by 530
- Nat.choosestatement and proof · cited by 494
- ProbabilityTheory.binomialstatement · cited by 20
- Set.finite_Iioproof · cited by 4
- Set.ncard_Iio_natproof · cited by 2
- ProbabilityTheory.map_ncard_setBernoulli_real_singletonproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- ProbabilityTheory.map_cast_binomial_real_singletonproof · cited by 3
- ProbabilityTheory.binomial_singletonproof · cited by 2
- ProbabilityTheory.binomial_real_selfproof · cited by 1
- ProbabilityTheory.binomial_real_zeroproof · cited by 1
- ProbabilityTheory.binomial_one_eq_bernoulliMeasureproof · cited by 0