Overview
Suppose that an urn contains n distinct balls of identical size and weight that are numbered
1, 2, 3, ..., n. An odd number (2m 1 ≤ n) of these balls are drawn out of the urn without
replacement. Let X be the random variable equal to the medium of the numbers on the
2m 1 balls drawn from the urn. The medium of an odd number of distinct numbers is the
middle number when these numbers are ordered from smallest to largest. For example, if 7
balls (m 3) are drawn yielding 3, 8, 2, 10, 12, 6, 18 and then reordered from smallest to
largest as 2, 3, 6, 8, 10, 12, 18, then X 8.