geometricPMFReal_nonneg — Mathlib

English

As in 169557, independence implies Gaussian sum with summed means and variances.

Русский

Как и в 169557, независимость даёт гауссиан с суммой параметров.

LaTeX

$$$\text{IndepFun } X Y P \rightarrow P\!\maxmap (X+Y) = \mathcal{N}(m_1+m_2, v_1+v_2).$$$

Lean4

theorem geometricPMFReal_nonneg {n : ℕ} (hp_pos : 0 < p) (hp_le_one : p ≤ 1) : 0 ≤ geometricPMFReal p n :=
  by
  rw [geometricPMFReal]
  have : 0 ≤ 1 - p := sub_nonneg.mpr hp_le_one
  positivity

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