An interval is a set of contiguous integers {a, a + 1, . . . , b} where a b. We use the notation [a, b] to denote the corresponding interval. Consider the following process for sampling a set of two distinct integers {i, j} that both lie in the base interval [1, n]: first, we choose two non-overlapping sub-intervals I J of [1, n]. Then, we sample integers i I and j J uniformly at random from each sub-interval. (a) Suppose we first deterministically choose two disjoint intervals I and J of [1, n], and then choose elements i I and j J uniformly at random from each sub-interval. Prove that the set {i, j} is is not uniformly distributed among all sets of two integers in [1, n]