[E] {9 points] Let K1, K2, ..., In be a random sample from the probability density function below [3(1) = 1,819.0 E I E 3 Consider two estimators for H: = ; = llm'inlfn, a; = Im'inl. It can be shown that both estimators are unbiased for B. but their efciencies are very different. Simulate 1ooo estimates d: and E"; if the true value of H = 4 and n = 1d. {a} Based on your simulated values argue that E and 31 are unbiased estimators, lb]: but that the relative efciency of lto g, :32; a; n2. (cl We know from homework and inspection of the likelihood for this density that Km\" is the mle for H, thus E is an unbiased estimator based on the mle. Clearly, d; is not an mle. Provide a concise but sufficient explanation based on estimator properties of why we would expect to observe [bi given we had established [a]