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December 13th, 2011, 02:15 PM  #1 
Newbie Joined: Dec 2011 Posts: 1 Thanks: 0  Weak convergence of the sum of dependent variables question
Hi guys, Problem: Let {Xn},{Yn}  realvalued random variables. {Xn}>{X}  weakly; {Yn}>{Y} weakly. Assume that Xn and Yn  independent for all n and that X and Y  are independent. Show that {Xn+Yn}>{X+Y} weakly. This can be shown using Levy's theorem and characteristic functions. Question: If independence does not hold, can you construct a counterexample? I appreciate any help in advance. 

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convergence, dependent, question, sum, variables, weak 
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