Let X = (X,,X,,. .,x,) be a random sample of size n>2 from a Poisson distribution with parameter ^. X1+X2 Two possible estimators of 1 are suggested by Â = t42 and î2 = X (the sample mean). Note: For this question you can make use of the distributions formula sheet. Calculate the bias and variance of each estimator.

Let X = (X,,X,,. .,x,) be a random sample of size n>2 from a Poisson distribution with parameter ^. X1+X2 Two possible estimators of 1 are suggested by Â = t42 and î2 = X (the sample mean). Note: For this question you can make use of the distributions formula sheet. Calculate the bias and variance of each estimator.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Estimator of Poisson Distribution

Let X = (X,, X, .,X,) be a random sample of size n22 from a Poisson distribution with
parameter 2.
X1+X2
Two possible estimators of 1 are suggested by = 42 and î2 = X (the sample mean).
%3D
2
Note: For this question you can make use of the distributions formula sheet.
Calculate the bias and variance of each estimator.
Calculate the Mean Square Error (MSE) of each estimator and determine which of these two
estimators is more efficient.
Show that î2 is the method of moments estimator (MME) of 2.

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