# Exercise Solution 4.2

- The first estimator is based upon the fact that, out of 50 realizations drawn from a
*U*(0,θ) distribution, we would expect the largest of those realizations to fall near the upper bound θ. The second estimator is based upon the fact that the mean of a*U*(0,θ) distribution is θ/2. Accordingly, multiplying the sample mean by 2 provides an estimate of θ. *H*_{1}estimates θ as 14.66.*H*_{2}estimates θ as 13.84.- No. Estimator
*H*_{1}produced an estimate that is clearly impossible. Since realization 14.66 was drawn from the interval (0,θ), it is impossible that θ equals 13.84. *H*_{1}is biased. It will always underestimate θ.*H*_{2}is unbiased.

This exercise illustrates the tradeoffs we often face in selecting a statistical estimator. In this case, estimator *H*_{1} is biased. It will always underestimate θ. On the other hand, estimator *H*_{2} is unbiased, but it can produce estimates that are clearly incorrect.

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