[6] (9 points) Let X1, X2, ..., Xn be a random sample from the probability density function below fx(x) = 1/2,0 sxse Con

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6 9 Points Let X1 X2 Xn Be A Random Sample From The Probability Density Function Below Fx X 1 2 0 Sxse Con 1 (55.08 KiB) Viewed 20 times

[6] (9 points) Let X1, X2, ..., Xn be a random sample from the probability density function below fx(x) = 1/2,0 sxse Consider two estimators for 8; = 1 = Xmax*(n+1)/n, ô2 = Xmin*(n+1). It can be shown that both estimators are unbiased for 6, but their efficiencies are very different. Simulate 1000 estimates ê, and Ôz if the true value of 0 = 4 and n = 10. (a) Based on your simulated values argue that ôn, and êŋ are unbiased estimators, (b) but that the relative efficiency of ê,to @z, Var(82) < nº. @ (c) We know from homework and inspection of the likelihood for this density that Xmax is the mle for e, thus ê, is an unbiased estimator based on the mle. Clearly, , is not an mle. Provide a concise but sufficient explanation based on estimator properties of why we would expect to observe (b) given we had established (a).