Monitor two consecutive packets going through a router. Classify each one as vid
ID: 3070695 • Letter: M
Question
Monitor two consecutive packets going through a router. Classify each one as video (v) if it was sent from a Youtube server or as ordinary data (d) otherwise. Your observation is a sequence of two letters (either v or d). For example, two video packets corresponds to vv. The two packets are independent and the probability that any one of them is a video packet is 0.8. Denote the identity of packet i by C. If packeti is a vided packet, then Civ; otherwise, Cd. Count the number Nv of video packets in the two packets you have observed. Determine whether the following pairs of events are independent: (a) {Nv 2) and {Nv 2 1) (b) (Nv 2 1 and C-v)Explanation / Answer
(a) Let A = { Nv = 2 } , B = { Nv>=1 }. Clearly, A and B are NOT independent events because if event A has occured, it means that Nv =2 , which also means that Nv >= 1, so event B is certain to occur. Thus, information about occurence of event A provides complete information about occurence of B. Hence they are not independent.
(b) Let C = { Nv>=1 }, D = { C1 = v }. C and D are NOT independent events because if event D has occured, it means that there will be atleast 1 video packet in the sequence of 2 packets and therefore Nv>=1, which implies that event C has also occured. So occurence of event D gives complete information about occurence of C. Therefore C and D are dependent.
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