Question: If X1 X2 and X3 constitute a random sample of
If X1, X2, and X3 constitute a random sample of size n = 3 from a normal population with the mean µ and the variance σ2, find the efficiency of X1 + 2X2 + X3 / 4 relative to X1 + X2 + X3 / 3 as estimates of µ.
Relevant QuestionsIf X1 and X2 constitute a random sample of size n = 2 from an exponential population, find the efficiency of 2Y1 relative to , where Y1 is the first order statistic and 2Y1 and are both unbiased estimators of the ...Since the variances of the mean and the midrange are not affected if the same constant is added to each observation, we can determine these variances for random samples of size 3 from the uniform population By referring ...Use the result of Example 8.4 on page 253 to show that for random samples of size n = 3 the median is a biased estimator of the parameter θ of an exponential population. 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 results of Theorem 8.1 on page 233 to show that 2 is an asymptotically unbiased estimator of µ2.
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