Theorems · Definition · probability
PMF.binomial
Deprecated since 2026-04-07Use ProbabilityTheory.binomial instead.
(p : NNReal) → p ≤ 1 → (n : ℕ) → PMF (Fin (n + 1))
The binomial PMF: the probability of observing exactly i “heads” in a sequence of n
independent coin tosses, each having probability p of coming up “heads”.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRealstatement and proof · cited by 4,310
- ENNReal.ofNNRealproof · cited by 1,279
- Nat.chooseproof · cited by 494
- PMFstatement · cited by 127
- PMF.ofFintypeproof · cited by 7
Cited by7
Results whose statement or proof uses this declaration.
- PMF.binomial_applystatement · cited by 4
- PMF.binomial_apply_laststatement · cited by 1
- PMF.binomial_apply_of_lestatement and proof · cited by 0
- PMF.binomial_apply_selfstatement · cited by 0
- PMF.binomial_apply_zerostatement · cited by 0
- PMF.binomial_one_eq_bernoullistatement · cited by 0
- PMF.binomial.congr_simpstatement and proof · cited by 0