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Let X be a Poisson random variable. If P(X = 1) equals P(X = 2), then the value of P(X = 4) is
- 1/(2e²)
- 1/(3e²)
- 2/(3e²)
- 1/e²
Correct answer: 2/(3e²)
Solution
For a Poisson variable, P(X=1)=P(X=2) means e^-L L = e^-L L^2/2, so L=2. Then P(X=4)=e^-2 * 2^4/4! = 16/(24 e^2) = 2/(3 e^2).
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