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A statistics class tosses a coin three times and lets X count the heads. Why is X called a discrete random variable?
ABecause it only ever equals exactly one
BBecause you can count its possible outcomes
CBecause coins always land heads half the time
DBecause three tosses is a large sample
Answer & Solution
Correct answer: B. Because you can count its possible outcomes
1. The three-coin example gives X the countable outcomes 0, 1, 2, 3 heads.
2. A variable is discrete exactly when its possible values can be counted and each outcome is random.
3. Option B restates that reasoning correctly, so it is the answer.
4. Options A, C, and D each describe something false or irrelevant about X, so none of them explain discreteness.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.1 Probability Distribution Function (PDF) for a Discrete Random Variable_
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