Question: 1.4. Both Theorem 5.4.1 and its complement in Exercise 2 above are best possible in the following sense. Let {all} and 0, Then there exists

1.4. Both Theorem 5.4.1 and its complement in Exercise 2 above are "best possible" in the following sense. Let {all} and

> 0, Then there exists a sequence of independent and identically distributed r.v.'s

{Xn} such that [(Xn) = 0, $(

[HINT: Make Ln gP{IXnl > an} = 00 by letting each Xn take two or three values only according as bnl 1.]

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