An alternative form of estimation is accomplished through

Chapter 1, Problem 9.99

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An alternative form of estimation is accomplished through the method of moments. This method involves equating the population mean and variance to the corresponding sample mean x and sample variance s2 and solving for the parameters, the results being the moment estimators. In the case of a single parameter, only the means are used. Give an argument that in the case of the Poisson distribution the maximum likelihood estimator and moment estimators are the same.

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