term𝔼[_|_] — Mathlib

English

Let X_i be a finite family of random variables that are pairwise independent and square-integrable. Then the variance of their sum equals the sum of their variances.

Русский

Пусть X_i — конечная семейство случайных величин, попарно независимы и квадрат-интегрируемы; тогда Var(∑ X_i) = ∑ Var(X_i).

LaTeX

$$$\operatorname{Var}\left[\sum_{i\in s} X_i;\, \mu\right] = \sum_{i\in s} \operatorname{Var}[X_i;\, \mu]$$$

Lean4

/-- `𝔼[f|m]` is the conditional expectation of `f` with respect to `m`. -/
@[scoped term_parser 1000]
public meta def «term𝔼[_|_]» : Lean.ParserDescr✝ :=
  ParserDescr.node✝ `ProbabilityTheory.«term𝔼[_|_]» 1024
    (ParserDescr.binary✝ `andthen
      (ParserDescr.binary✝ `andthen
        (ParserDescr.binary✝ `andthen
          (ParserDescr.binary✝ `andthen (ParserDescr.symbol✝ "𝔼[") (ParserDescr.cat✝ `term 0))
          (ParserDescr.symbol✝ "|"))
        (ParserDescr.cat✝ `term 0))
      (ParserDescr.symbol✝ "]"))

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