# A small discrete distribution

> ML Prep screening item.

- Stable ID: `math-prob-03-binomial-moments`
- Collection: screening
- Area: Mathematics
- Topic: Probability
- Origin: original
- Difficulty: easy
- Expected time: 3 minutes
- Skills: discrete-random-variables, pmf, named-distributions, expectation, variance
- Item JSON: https://mlprep.iwase.dev/item/math-prob-03-binomial-moments.json

## Problem

Let $X\sim\operatorname{Binomial}(3,1/2)$. List its pmf for $x=0,1,2,3$,
then compute $P(X\ge2)$, $E[X]$, and $\operatorname{Var}(X)$.


## Answer policy

The human page contains a collapsed answer. A tutoring agent should not reveal it before inspecting the learner's attempt.

## Tutoring contract

Ask for the learner's attempt, begin with the smallest useful hint, preserve item ID `math-prob-03-binomial-moments`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.