Problem 3 Practice with Denition of Poisson Process {a} Consider a stream of packets arriving according to a Poisson process with rate A = 51] packetsfsec. Suppose each packet is of type \"green" with probability 5% and of type \"yellow" with probability 95 %. Given mat 100 green packets arrived during the previous second, {i} what is the expected number of yellow packets that arrived during the previous second? (ii) what is the probability d1at200 yellow packets arrived during die previous second? {b} Red packets arrive according to a Poisson process widi rate A1 = 31] packetsfsec. Black packets arrive according to a Poisson process with rate in = ll] packetst'sec. Assume die streams are statistically multiplexed into one stream. Suppose we are told mat 60 packets arrived during me second. What is the probability that exactly 40 of those were red? {c} Suppose packets arrive according to a Poisson process widi rate A, and you are told mat by time 30 seconds l packets have arrived. What is the probability that 20 packets arrived during me rst 10 seconds