Theorems · Theorem · probability
ProbabilityTheory.map_cast_binomial_real_singleton
∀ {R : Type u_1} [inst : MeasurableSpace R] [inst_1 : AddMonoidWithOne R] [MeasurableSingletonClass R] [CharZero R]
(n k : ℕ) (p : ↑unitInterval),
(MeasureTheory.Measure.map Nat.cast (ProbabilityTheory.binomial n p)).real {↑k} =
↑(n.choose k) * ↑p ^ k * (1 - ↑p) ^ (n - k)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 291 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measureproof · cited by 10,939
- Set.Elemstatement and proof · cited by 7,166
- Set.preimageproof · cited by 4,946
- Set.extproof · cited by 2,266
- CharZerostatement and proof · cited by 932
- MeasureTheory.Measure.mapstatement · cited by 858
- unitIntervalstatement and proof · cited by 607
- MeasureTheory.Measure.realstatement and proof · cited by 530
- Nat.choosestatement and proof · cited by 494
Cited by3
Results whose statement or proof uses this declaration.
- ProbabilityTheory.map_cast_binomial_real_selfproof · cited by 0
- ProbabilityTheory.map_cast_binomial_real_zeroproof · cited by 0
- ProbabilityTheory.map_cast_binomial_singletonproof · cited by 0