Question: Let Yl , ... , Yn be a random sample from a population with distribution Y Exponential(), 1 Y/ and cdf Fy(y) = where

Let Yl , ... , Yn be a random sample from a population with distribution Y Exponential(), 1 Y/ and cdf Fy(y) = where 43 is unknown. Recall then Y has pdf f (y) = e 1 ey/ for y 0, where EY = 5 and Vary = "2. Let Y(l) = min(Y1,... , Yn) be the first ordered statistic for the random sample. (a) Show Y(l) Exponential(/n), and show nY(1) is an unbiased estimator of /3. Hint: Use Homework 1 to determine the cdf of Y(l).

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