Theorems · Theorem · probability
Finset.expect_eq_sum_div_card
∀ {ι : Type u_1} {K : Type u_3} [inst : Semifield K] [inst_1 : CharZero K] (s : Finset ι) (f : ι → K),
(s.expect fun i => f i) = (∑ i ∈ s, f i) / ↑s.card- Defined in
- Mathlib.Algebra.BigOperators.Expect
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Finset.sumstatement and proof · cited by 5,195
- Finset.cardstatement and proof · cited by 2,327
- CharZerostatement and proof · cited by 932
- NNRatstatement · cited by 523
- Semifieldstatement and proof · cited by 439
- NNRat.castproof · cited by 235
- div_eq_inv_mulproof · cited by 146
- Finset.expectstatement · cited by 116
- NNRat.cast_natCastproof · cited by 31
- NNRat.smul_defproof · cited by 7
- NNRat.cast_invproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Fintype.expect_eq_sum_div_cardproof · cited by 1
- Real.compact_inner_le_weight_mul_Lp_of_nonnegproof · cited by 0