2. Law of Large Numbers Recall that the Law of Large Numbers holds if, for every 8 > 0, mm gs, ]E(%Sn)| > e] = 0. In class, we saw that the Law of Large Numbers holds for 5,, 2 X1 + - - - +Xn, where the Xi's are i.i.d. random variables. This problem explores if the Law of Large Numbers holds under other circumstances. Packets are sent from a source to a destination node over the Internet. Each packet is sent on a certain route, and the routes are disjoint. Each route has a failure probability of p and different routes fail independently. If a route fails, all packets sent along that route are lost. You can assume that the routing protocol has no knowledge of which route fails. For each of the following routing protocols, determine whether the Law of Large Numbers holds when Sn is dened as the total number of received packets out of n packets sent. Answer Yes if the Law of Large Number holds, or No if not, and give a brief justication of your answer. (Whenever convenient, you can assume that n is even.) (a) Yes or No: Each packet is sent on a completely different route. (b) Yes or No: The packets are split into n / 2 pairs of packets. Each pair is sent together on its own route (i.e., different pairs are sent on different routes). (c) Yes or No: The packets are split into 2 groups of 11/2 packets. All the packets in each group are sent on the same route, and the two groups are sent on different routes. (d) Yes or No: All the packets are sent on one route