A box has an unknown odd number of balls labeled consecutively as -θ, -(θ - 1), ..., -2, -1, 0, 1, 2, ...,(θ - 1), θ, where θ is an unknown nonnegative integer. A simple random sample X1, ..., Xn is taken without replacement, where Xi is the label on the ith ball selected and n < 2θ="" +="" 1.="">
(a) Find a statistic that is minimal sufficient for θ and derive its distribution.
(b) Show that the minimal sufficient statistic in (a) is also complete.