Subtopic: Poisson, normal and binomial distributions
Question Statement:
The probability function value [f(x)] at x = 3 for Poisson distribution with mean of 2 is
Options:
(A) 0.12
(B) 0.18
(C) 0.24
(D) 0.30
Official Answer Key:
B
Step-by-Step Solution & Explanation
Poisson pmf: f(x) = e^-λ λ^x / x!, with λ = 2, x = 3. f(3) = e^-2 · 2^3 / 3! = 0.1353 × 8 / 6 = 1.0827/6 = 0.1804 ≈ 0.18. This matches option (B). Option (C) 0.24 would result from omitting the 3! in the denominator (using x! = 4 by mistake), and (A) results from using λ=1.
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