2. Let X₁, X2, Xn represent a random sample from a Poisson distribution with probability mass function given below. p(x) = e-> ette x! " X x = = 0, 1, 2, ... (a) Look up the Special Distributions summary sheet on Moodle and state E(X). (b) Find the moment estimator of X. (c) Show that the maximum likelihood estimator of X is the same as the moment estimator. (d) Estimate A from the following observations using the moment/maximum likelihood estimator. Round your answer to 4 decimal places. 0 1 2 3 4 567 Frequency 18 37 42 30 13 7 2 1

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