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Mathematical Statistics with Applications
We can place a 2-standard-deviation bound on the error of estimation with any estimator for which we can find a reasonable estimate of the standard error. Suppose that $Y_{1}, Y_{2}, \ldots, Y_{n}$ represent a random sample from a Poisson distribution with mean $\lambda$. We know that $V\left(Y_{i}\right)=\lambda$, and hence $E(\bar{Y})=\lambda$ and $V(\bar{Y})=\lambda / n .$ How would you employ $Y_{1}, Y_{2}, \ldots, Y_{n}$ to estimate $\lambda ?$ How would you estimate the standard error of your estimator?
