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.
Answer to relevant QuestionsSubstituting “asymptotically unbiased” for “ unbiased” in Theorem 10.3, use this theorem to rework Exercise 10.35. After referring to Example 10.4, is the nth order statistic, Yn, a sufficient estimator of the parameter β? If X1, X2, . . . , Xn constitute a random sample of size n from a population given by Find estimators for ∂ and θ by the method of moments. This distribution is sometimes referred to as the two-parameter exponential ...If X1, X2, . . . , Xn constitute a random sample of size n from a geometric population, find formulas for estimating its parameter α by using (a) The method of moments; (b) The method of maximum likelihood. If V1, V2, . . . , Vn1 and W1, W2, . . . , Wn2 are independent random samples of sizes n1 and n2 from normal populations with the means µ1 and µ2 and the common variance σ2, find maximum likelihood estimators for µ1, ...
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