Theorems · Theorem · probability
ProbabilityTheory.map_cast_binomial_eq_sum_dirac
∀ {R : Type u_1} [inst : MeasurableSpace R] [inst_1 : AddMonoidWithOne R] [MeasurableSingletonClass R] (n : ℕ)
(p : ↑unitInterval),
MeasureTheory.Measure.map Nat.cast (ProbabilityTheory.binomial n p) =
∑ k ≤ n, ENNReal.ofReal (↑(n.choose k) * ↑p ^ k * (1 - ↑p) ^ (n - k)) • MeasureTheory.Measure.dirac ↑k- Cited by
- 1 results in Mathlib
- Foundations
- Depth 293 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Set.Elemstatement and proof · cited by 7,166
- Finset.sumstatement and proof · cited by 5,195
- Finset.sum_congrproof · cited by 2,323
- ENNReal.ofRealstatement and proof · cited by 863
- MeasureTheory.Measure.mapstatement and proof · cited by 858
- unitIntervalstatement and proof · cited by 607
- Nat.choosestatement and proof · cited by 494
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.integrable_map_cast_binomialproof · cited by 2