Let (N1,...,Nm) be the outcome vector for a multinomial experiment with n trials and m categories. Prove that Pr(N1 ≤ t1,...,Nm ≤ tm) ≤ m i=1 Pr(Ni ≤ ti) (4.7)

Pr(N1 ≥ t1,...,Nm ≥ tm) ≤ m i=1 Pr(Ni ≥ ti) (4.8)

for all integers t1,...,tm. If all tk = 0 in (4.8) except for ti and tj , conclude that Pr(Ni ≥ ti, Nj ≥ tj ) ≤ Pr(Ni ≥ ti) Pr(Nj ≥ tj )