Let X1,X2,…Xn be a random sample of size n form a uniform distribution on the interval [θ1,θ2]. Let Y = min (X1,X2,…,Xn).
(a) Find the density function for Y. (Hint: find the cdf and then differentiate.)
(b) Compute the expectation of Y.
(c) Suppose θ1= 0. Use part (b) to give an unbiased estimator for θ2.
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