Question: Let {Xn : n 1} be a sequence of random variables and Sn = X1+ ... +Xn. Show that if Xn 0 in L1, then

Let {Xn : n 1} be a sequence of random variables and Sn = X1+ ... +Xn.

Show that if Xn 0 in L1, then Sn=n 0 in L1.

Provide an example where Xn0 in probability, but Sn/n does not converge to 0 in probability.

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