Let X1, ...,Xn be a random sample from the U(0,) distribution. Find: (i) E(Xm 1:n) and E(Xm n:n). (ii) E(Xn:n|X1:n). (iii) The cdf of variable

Let X1, ...,Xn be a random sample from the U(0,θ) distribution. Find: (i) E(Xm 1:n)

and E(Xm n:n). (ii) E(Xn:n|X1:n). (iii) The cdf of variable V = Xn:n − X1:n. (iv) The probability that the interval [X1:n,Xn:n] does not include a given point x0. (v) The point x0 for which the probability in part (iv) is the smallest.