Using the notation of this section, let U be the number of observed values of X in the smallest d items of the combined sample of m + n items.
Argue that
Pr (U = u) = ( )(d:u)/( m ;"). u = 0, 1, . . . , m.
The statistic U could be used to test the equality of the (lOOp)th percentiles, where (m + n)p = d, of the distributions of X and Y.