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A Poisson random variable is written X ~ P(μ). What are the mean, variance, and standard deviation of X in terms of μ?
AMean μ, variance μ^2, standard deviation μ
BMean sqrt(μ), variance μ, standard deviation μ
CMean μ, variance μ, standard deviation sqrt(μ)
DMean μ^2, variance μ, standard deviation sqrt(μ)
Answer & Solution
Correct answer: C. Mean μ, variance μ, standard deviation sqrt(μ)
1. For a Poisson distribution, the parameter μ is itself the mean of X.
2. The variance also equals μ, an unusual feature unique to the Poisson distribution.
3. The standard deviation is the square root of the variance, so σ = sqrt(μ).
4. Options A, B, and D each misplace where μ or its square root belongs among mean, variance, and standard deviation.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.6 Poisson Distribution_
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