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Let Y1,Y2,Y3,...,Yn denote a random sample from a Poisson probability distribution. (a) Show that sample mean,...

Let Y1,Y2,Y3,...,Yn denote a random sample from a Poisson probability distribution.

(a) Show that sample mean, ˆ θ1 = ¯ Y and the sample variance, ˆ θ2 = S2 are both unbiased estimators of θ.

(b) Calculate relative efficiency of the two estimators in (a). Based on your calculation, Which of the two estimators in 3a would you select as a better estimator?

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