Let X 1 , X 2 ,. X n be a random sample of size n form a uniform distribution on the interval [ 1 , 2 ]. Let Y = min ( X 1 , X 2 ,., X n ). (a) Find...

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.