36. Let Xl •. ..• x" be i.i.d. with cumulative distribution function F. let al < ' " < am -I be any given real numbers. and let ao = - 00, am = 00 . If "; is the number of X's in (aj_l , aj), the X2-test (43) can be used to test H : F = Fo with 'fTj = Fo(a j) - Fo(a j_l ) for i = 1. .. . , m. (i) Unlike the Kolmogorov test, this x2 -test is not consistent against all FI '* Fo as n -> 00 with the a's remaining fixed. (ii) The test is consistent against any FI for which FI(a;) - FI(aj_l) '* Fo(a;} - fQ(a;-d for at least one i.