1. Let Ymin be the smallest order statistic in random sample of size n drawn from the uniform pdf, f sub Y (y; ?) = 1/?, 0 ? y ? ?. Find an unbiased estimator for ? based on Ymin.
2. We showed in Example 5.4.4 that ˆsigma2 = (1/n) (sum i=1 to n) (Yi - Y bar)2 is biased for sigma2. Suppose mu is known and does not have to be estimated by Y bar. Show that (sigma hat) ˆsigma2 = (1/n) (sum i=1 to n) (Yi - mu)2 is unbiased for sigma2.