Summary: Math­571. 5­th Homework. Due Tuesday, April 10, 2007.
1. Let {Xn} be a sequence of r.v.'s. Let Sn = n
j=1 Xj. Let p 1. Show that:
(i) Xn
a.s.
0 implies Sn
n
a.s.
0.
(ii) Xn
Lp
0 implies Sn
n
Lp
0.
(iii) Xn
P
0 does not imply Sn
n
P

Source: Arcones, Miguel A. - Department of Mathematical Sciences, State University of New York at Binghamton

Collections: Mathematics