Question

1. Consider a random sample X?, X?, ..., X? from a Poisson distribution with mean ?. (a) Find the method of moments estimator of ?. (b) Find the maximum likelihood estimator of ?. (c) An estimator ?? is said to be consistent if for any ? > 0, lim n?? P(|?? - ?| ? ?) = 0. That is, ?? is consistent if, as the sample size gets larger, it is less and less likely that ?? will be further than ? from the true value of ?. Use Chebyshev's inequality to show that the maximum likelihood estimator of ? is a consistent estimator of ?.

          1. Consider a random sample X?, X?, ..., X? from a Poisson distribution with mean ?.
(a) Find the method of moments estimator of ?.
(b) Find the maximum likelihood estimator of ?.
(c) An estimator ?? is said to be consistent if for any ? > 0, lim n?? P(|?? - ?| ? ?) = 0. That is, ?? is consistent if, as the sample size gets larger, it is less and less likely that ?? will be further than ? from the true value of ?. Use Chebyshev's inequality to show that the maximum likelihood estimator of ? is a consistent estimator of ?.

1. Consider a random sample X?, X?, ..., X? from a Poisson distribution with mean ?.
(a) Find the method of moments estimator of ?.
(b) Find the maximum likelihood estimator of ?.
(c) An estimator ?? is said to be consistent if for any ? > 0, lim n?? P(|?? - ?| ? ?) = 0. That is, ?? is consistent if, as the sample size gets larger, it is less and less likely that ?? will be further than ? from the true value of ?. Use Chebyshev's inequality to show that the maximum likelihood estimator of ? is a consistent estimator of ?.

Added by Rebecca L.

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