5. (i) Let X1, X2, ..., Xn,... be i.i.d. random variables with mean 0 and finite variance o2 > 0. Show that X1X2+ X2X3 + ... + Xn-1Xn n converges to a limit in probability that you need to identify. (ii) For any fixed positive integer m write a rough argument (exact technical details are not required) as to why X1X2X3 . ..Xm + X2X3 . .. Xml+ . ..+ Xn-m+1Xn-m+2 .. . Xn n converges to the same limit