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The second moment of a Poisson-distributed random variable is 2. The mean of the variable is ....

My question on solving we get 2 values of lamda(ie mean) .One is -2 and the other is 1 .So which one to choose?

The second moment of Poisson Distribution is:

Here we have, $\lambda^2+\lambda =2$. Solving we get, $\lambda = -2,1$.

The average number of events in an interval is designated $\lambda$ (lambda). Lambda is the event rate, also called the rate parameter. Since the number of events cannot be $-ve$, the answer should be clear.

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