If the number of weekly accidents occurring on a mile stretch of a particular road follows a Poisson distribution with parameter λ . Then

(i) Find the Cramer-Rao lower bound for the variance.

(ii) Also, find the UMVUE of λ .

In this problem, we are given that the number of weekly accidents occurring on a mile stretch of a particular road follows a Poisson distribution with parameter λ. We are tasked with finding the Cramer-Rao lower bound (CRLB) for the variance and also the UMVUE (Uniformly Minimum Variance Unbiased Estimator) of λ.

(i) Cramer-Rao Lower Bound (CRLB) for the Variance

To find the Cramer-Rao lower bound, we first need to recall the general formula for the CRLB. The CRLB provides a lower bound for the variance of any unbiased estimator of a parameter. The CRLB for an unbiased estimator θ^\hat{\theta} of a parameter __________ __________ ___ ________ ___ _____.
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