In: Math
2. Alice and 10 other users are sending packets using the pure ALOHA protocol. The duration of a packet is 40 msec. Each user sends a packet (including both originals and retransmissions) following a Poisson process with rate 1/400 packets/msec.
(a) What is the chance of success on Alice’ first attempt? (hint: the probability that there is no othertransmission within the vulnerable period of Alice’s attempt)
(b) What is the probability that Alice gets exactly k collisions and then a success? (hint: consider a Bernoulli trials process)
(c) What is the expected number of transmission attempts needed to successfully send a packet?