Question: 1.1 {U (ISn I) 2 l' @ ( S: ) ~ 1m (c r::: = 1m (0 r::: = -(J 11--+00 V n n--+oo V

1.1· {U

(ISn I) 2 l' @ (

S: ) ~ 1m (c r::: = 1m (0 r::: = -(J 11--+00 V n n--+oo V n 7f

[If we assume only q7>{X 1 #-o} > 0, £'( IX 11) < 00 and £'(X 1) = 0, then we have t(IS n I) > C.fii for some constant C and all n; this is known as Hornich's inequality.] [HINT: In case (J2 = 00, if limn 0'(1 Sn/.fii) < 00, then there exists {nd such that Sn/ ~ converges in distribution; use an extension of Exercise 1 to show If(t/ .fii)12n -+ 0. This is due to P. Matthews.]

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