GATE 2016 EC – Question 12
The second moment of a Poisson-distributed random variable is 2. The mean of the random variable is ________
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Correct answer: 0.9 to 1.1
Explanation
For a Poisson variable with mean $\lambda$, the variance is $\lambda$, so the second moment is $\lambda + \lambda^2$. Setting $\lambda + \lambda^2 = 2$ gives $(\lambda + 2)(\lambda - 1) = 0$, and since the mean is positive, $\lambda = 1$.