Question: Show that the mean of a random sample of size
Show that the mean of a random sample of size n is a minimum variance unbiased estimator of the parameter λ of a Poisson population.
Relevant QuestionsIf Θ1 and Θ2 are independent unbiased estimators of a given parameter θ and var(Θ1) = 3 ∙ var(Θ2), find the constants a1 and a2 such that a1Θ1 + a2Θ2 is an unbiased estimator with minimum variance for such a linear ...If 1 is the mean of a random sample of size n from a normal population with the mean µ and the variance σ21, 2 is the mean of a random sample of size n from a normal population with the mean µ and the variance σ22, and ...With reference to Example 10.3, we showed on page 281 that – 1 is an unbiased estimator of d, and in Exercise 10.8 the reader was asked to find another unbiased estimator of d based on the smallest sample value. Find the ...With reference to the uniform population of Example 10.4, use the definition of consistency to show that Yn, the nth order statistic, is a consistent estimator of the parameter β. Example 10.4 If X1, X2, . . . , Xn ...If X1 and X2 constitute a random sample of size n = 2 from a Poisson population, show that the mean of the sample is a sufficient estimator of the parameter λ.
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