Assume the joint distribution of p-values is PRDS on the set I of true null hypotheses.

(i) Show that, for any increasing set D, P{(pˆ1,..., pˆs) ∈ D| ˆpi ≤ u} (9.142)
is nondecreasing in u for any i ∈ I.
(ii) More generally, show that E 
(pˆ1,..., pˆs) | ˆpi ≤ u 
is nondecreasing in j for any i ∈ I and any increasing (coordinate-wise) function .