# Question: If 1 X n 2 X 1

If Θ1 = X/n , Θ2 = X + 1 / n+ 2 , and Θ3 = 1/3 are estimators of the parameter θ of a binomial population and θ = 1/2 , for what values of n is

(a) The mean square error of Θ2 less than the variance of Θ1;

(b) The mean square error of Θ3 less than the variance of Θ1?

(a) The mean square error of Θ2 less than the variance of Θ1;

(b) The mean square error of Θ3 less than the variance of Θ1?

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Use Definition 10.5 to show that Y1, the first order statistic, is a consistent estimator of the parameter α of a uniform population with β = α + 1. Definition 10.5 The statistic is a consistent estimator of the ...Substituting “asymptotically unbiased” for “ unbiased” in Theorem 10.3, use this theorem to rework Exercise 10.35. If X1, X2, and X3 constitute a random sample of size n = 3 from a Bernoulli population, show that Y = X1 + 2X2 + X3 is not a sufficient estimator of θ. Consider special values of X1, X2, and X3.) Use the method of maximum likelihood to rework Exercise 10.53. In exercise Given a random sample of size n from a Poisson population, use the method of moments to obtain an estimator for the parameter λ. Use the method of maximum likelihood to rework Exercise 10.57.Post your question