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The probability of a defective computer component is 0.02, so X ~ G(0.02) counts components tested until the first defect. What are the mean and standard deviation of X?
Aμ = 50, σ ≈ 2450
Bμ = 0.02, σ ≈ 49.50
Cμ = 50, σ ≈ 49.50
Dμ = 2, σ ≈ 49.50
Answer & Solution
Correct answer: C. μ = 50, σ ≈ 49.50
1. μ = 1/p = 1/0.02 = 50 components tested, on average, until a defect appears.
2. Variance is (1/p)(1/p - 1) = (50)(49) = 2450.
3. σ = sqrt(2450) ≈ 49.50.
4. Option A reports the variance in place of the standard deviation, and option D shrinks the mean incorrectly.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.4 Geometric Distribution_
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