Question

2. Suppose you decide to randomly generate numbers from X ~ Unif (0,0). Your friend will ask for n numbers and then use this information to guess what value you (secretly) chose for θ. Typically, one might use θMLE-max Xi-X, to estimate θ. Your friend, however, has meganumerophobia, and is afraid to say the maximum number in the random sample. Instead he'll say the second largest number: θ-Xn-1. Determine the bias of this estimator by carefully finding the density function for X-1 and continuing from there. If the estimator is biased, check if it is asymptotically unbiased, and also modify it to create a new unbiased estimator

Answer 1

2 Xn-1) is he 2nd La rmge st mum ber sharishie Cn-

X n-)is biased (M-1) asymtohically unbiased, ,s の. Syvn un biase n-1) n- unbiased eshimatoY is nt n-I