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If a Poisson process has mean 4 customers per hour, probability of exactly 2 customers in an hour is
Ae⁻⁴ × 16 / 2
Be⁻⁴ × 8
Ce⁻² × 4
De⁻⁴ × 16 / 4
Answer & Solution
Correct answer: A. e⁻⁴ × 16 / 2
1. Poisson PMF: P(X=k) = e⁻λ × λᵏ / k!.
2. λ = 4, k = 2 ⇒ P = e⁻⁴ × 4² / 2! = e⁻⁴ × 16 / 2 = 8e⁻⁴.
3. Numeric: 8 × 0.0183 ≈ 0.1465.
4. Hence (A) matches the formula.
_Source: Maharashtra Balbharati Std XII Mathematics & Statistics (Commerce), Ch 8 "Probability Distributions", §8.2 ¶§8.2_
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