If X is a Poisson random variable with mean 3, then P(|X − 3| < 1) will be:
2019
If X is a Poisson random variable with mean 3, then P(|X − 3| < 1) will be:
- A.
(9e⁻³) / 2
- B.
(e⁻³) / 2
- C.
3e⁻³
- D.
(99e⁻³) / 8
Attempted by 102 students.
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Correct answer: A
Interpretation: |X − 3| < 1 means X must be strictly within 1 unit of 3. For a discrete (integer-valued) Poisson random variable, the only integer that satisfies this is X = 3.
Compute the probability at X = 3 using the Poisson PMF:
P(X = 3) = e^{−3} * 3^{3} / 3!.
Simplify: 3^{3} = 27 and 3! = 6, so 27/6 = 9/2.
Final answer: P(|X − 3| < 1) = P(X = 3) = (9 e^{−3})/2.