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lean_workbook_plus_62336

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

If there are nnn possibilities that occur with probabilities p1,p2,p3,…,pnp_1,p_2,p_3,\ldots,p_np1​,p2​,p3​,…,pn​ that are all-encompassing (so p1+p2+⋯+pn=1p_1+p_2+\cdots+p_n=1p1​+p2​+⋯+pn​=1) that have values e1,e2,e3,…,ene_1,e_2,e_3,\ldots,e_ne1​,e2​,e3​,…,en​ if they occur, then the expected value is defined as E=p1e1+p2e2+⋯+pkekE=p_1e_1+p_2e_2+\cdots+p_ke_kE=p1​e1​+p2​e2​+⋯+pk​ek​.

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_62336 {n : ℕ} (p e : Fin n → ℝ) (hp : ∑ i, p i = 1) : ∃ k, ∑ i, p i * e i = k   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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