Add exact-first stats/probability helper surface

[sacchen]

Add a focused stats/probability toolkit that matches phil's terminal-first, exact-by-default philosophy.

Scope Boundary

This issue is for stats and probability only.

• Number theory track lives in: Exact arithmetic ergonomics pack: gcd/lcm + core number-theory helpers #1
• Broader CS/applied-math (non-stats) lives in: Define CS/applied-math feature track (excluding #1/#4) #3
• Prioritization/meta planning lives in: Umbrella: prioritize math branch roadmap across feature tracks #6

Goal

Provide practical stats/probability helpers with explicit assumptions and stable scriptable output.

Proposed Scope

First wave

• Counting/combinatorics helpers: nCr, nPr aliases.
• Descriptive stats: mean, variance, stddev with explicit sample/population semantics.
• Binomial helpers (PMF/CDF) and z-score utility.

Follow-up

• Poisson and normal helper utilities.
• Core inference helpers (confidence intervals and basic test utilities).

Product Constraints

• Exact results where feasible.
• Explicitly signal numeric approximation when exact form is not retained.
• Keep one-shot and REPL output behavior aligned.
• Keep JSON output stable and deterministic.

Acceptance Criteria

• First-wave helper set is implemented and documented with examples.
• Ambiguous semantics are avoided (sample vs population must be explicit).
• Unit/integration/regression tests cover core workflows and error hints.

Non-Goals

• Full statistical package parity.
• Auto-inference with implicit assumptions.

Test Gate

• uv run --group dev pytest
• uv run --group dev pytest --cov=calc --cov-report=term-missing --cov-fail-under=90

[sacchen]

Dependency/implementation note: #8 proposes using SymPy-native APIs across internals and explicitly calls out for this track, to avoid hand-rolled probability/stat formulas.

[sacchen]

Correction to prior note: #8 explicitly recommends using sympy.stats in this track to avoid hand-rolled probability/stat formulas.

[sacchen]

Roadmap status update (from #6): this is currently Next after #7 and #8 complete their phase-1 reliability/foundation work.

[sacchen]

Linked strategy anchor: #9 (Product principles and design decision framework).

When #4 moves forward, use #9 for exactness policy, ambiguity handling, and release-scope discipline.