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Math Help - converges almost surely

  1. #1
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    converges almost surely

    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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  2. #2
    Junior Member frenzy's Avatar
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    Quote Originally Posted by economics View Post
    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 X_1,X_2,\ldots are iid and have finite expectation then

    \sum_n\frac{X_n}{n} converges a.s. by the SLLN. This implies your problem
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