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Let X1, . . . , Xn be i.i.d from pmf f(x|λ) where f(x) = (e^(−λ)*(λ^x))/x!,...

Let X1, . . . , Xn be i.i.d from pmf f(x|λ) where f(x) = (e^(−λ)*(λ^x))/x!, λ > 0, x = 0, 1, 2

a) Find MoM (Method of Moments) estimator for λ

b) Show that MoM estimator you found in (a) is minimal sufficient for λ

c) Now we split the sample into two parts, X1, . . . , Xm and Xm+1, . . . , Xn. Show that ( Sum of Xi from 1 to m, Sum of Xi from m+1 to n) is sufficient for λ.

d) Does the estimator in (a) achieve Cramer-Rao lower bound? Justify your answer

e) What is asymptotic distribution of MoM estimator you found in (a)?

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