Unformatted text preview: he calculations in part c lead to convergence in distribution of
∑
√ via the generalized CLT. Problem 6 (17 pts). Let
∑ , a. (7 points)

(I) ∑ Let
 Hint: Are the
(I) represents. be random variables and denote
. Prove:
(I), where
a {
}     events in (I) disjoint? Try to express in words what From now on assume that
b. (6 points)
Prove: (I)
a are independent.
 c. (4 points)

If converge in probability then a
probability as
∞.


Hint: Prove first that
Then combine parts a and b.
Remark: It follows from part c that
converge a.s.  
as  in
∞....
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 Spring '12
 STAFF
 Probability, Probability theory

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