an appropriate 100(1-a)% confidence interval for poisson parameter lambda is
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For Poisson, the mean and the variance are both $\lambda$. If you want the confidence interval around lambda, you can calculate the standard error as $\sqrt{\lambda / n}$.
The 95-percent confidence interval is $\hat{\lambda} \pm 1.96\sqrt{\hat{\lambda} / n}$.
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Step-by-step An appropriate 100(1-a)% confidence interval for poisson parameter lambda is:
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