The Second Moment of a Poisson-distributed random variable is 2. Then the Mean…
2024
The Second Moment of a Poisson-distributed random variable is 2. Then the Mean of the random variable is _______.
- A.
0
- B.
1
- C.
10
- D.
5
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Correct answer: B
Let the Poisson parameter and mean be lambda. For a Poisson random variable, Var(X) = lambda and E[X] = lambda. Therefore E[X^2] = Var(X) + (E[X])^2 = lambda + lambda^2. Given E[X^2] = 2, we get lambda^2 + lambda - 2 = 0, so (lambda - 1)(lambda + 2) = 0. Since a Poisson mean cannot be negative, lambda = 1.