Let X1, X2,... be iid having expected value and a symmetric distribution P(X1>x)=P(X1<-x) for all x. Show that SUM_n (Xn/n) converges almost surely.
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Originally Posted by economics Let X1, X2,... be iid having expected value and a symmetric distribution P(X1>x)=P(X1<-x) for all x. Show that SUM_n (Xn/n) converges almost surely. If are iid and have finite expectation then converges a.s. by the SLLN. This implies your problem
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