Let X1,...,Xn ∼ iid Pois(θ), and we wish to estimate φ = Pθ(X = 0) = e−θ. Consider Yi = I (Xi = 0). Show that ∑ni=1 Yi follows a Bin(n, φ) distribution. (d)  Using Y1 , . . . , Yn find an unbiased estimator for φ. (e)  Is the estimator in (d) the MLE for φ?

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