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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?

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?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Let X1,...,Xn ∼ iid Pois(θ), and we wish to estimate φ = Pθ(X = 0) = e−θ.

  1. Consider Yi = I (Xi = 0). Show that ∑ni=1 Yi follows a Bin(n, φ) distribution.

  2. (d)  Using Y1 , . . . , Yn find an unbiased estimator for φ.

  3. (e)  Is the estimator in (d) the MLE for φ?

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