Theorems · Theorem · probability

ProbabilityTheory.integral_map_cast_binomial

∀ {R : Type u_1} [inst : MeasurableSpace R] [inst_1 : AddMonoidWithOne R] {n : ℕ} {p : ↑unitInterval} {E : Type u_3}
  [inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace ℝ E] [CompleteSpace E] [MeasurableSingletonClass R] (f : R → E),
  ∫ (x : R), f x ∂MeasureTheory.Measure.map Nat.cast (ProbabilityTheory.binomial n p) =
    ∑ k ≤ n, (↑(n.choose k) * ↑p ^ k * (1 - ↑p) ^ (n - k)) • f ↑k

Defined in

Mathlib.Probability.Distributions.Binomial

Cited by

0 results in Mathlib

Foundations

Depth 295 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceAddMonoidWithOneNormedAddCommGroupNormedSpaceCompleteSpaceMeasurableSingletonClass