Question: Pls help with this 3. Consider a Poisson random sample X1, ..., X, ~ Pois (A). (a) Find the method of moments estimator for A.

Pls help with this

3. Consider a Poisson random sample X1, ..., X, ~ Pois (A). (a) Find the method of moments estimator for A. [3] (b) Write down the likelihood and log-likelihood for the model. [5] (c) Find the score function and the observed Fisher information function. [4] (d) Find the maximum likelihood estimator (MLE) for A. [5] (e) Check whether the MLE is unbiased for A. (f) Find the variance of the MLE. (g) Check whether the MLE attains the Cramer-Rao lower bound. [4] [27]

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