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For a geometric random variable X ~ G(p), formulas exist for its mean and standard deviation. What are they?
Aμ = np, σ = sqrt(npq)
Bμ = 1/p, σ = sqrt((1/p)(1/p-1))
Cμ = p, σ = sqrt(p(1-p))
Dμ = 1/p, and σ = 1/p exactly
Answer & Solution
Correct answer: B. μ = 1/p, σ = sqrt((1/p)(1/p-1))
1. The geometric distribution's mean formula is μ = 1/p.
2. Its standard deviation formula is σ = sqrt((1/p)(1/p - 1)).
3. Together these give the expected number of trials until success and how much that count typically varies.
4. Option A lists the binomial formulas instead, and option C mistakes p for the mean itself.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.4 Geometric Distribution_
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