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2. Alice and 10 other users are sending packets using the pure ALOHA protocol. The duration...

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Basic Math

2. Alice and 10 other users are sending packets using the pureALOHA protocol. The duration of a packet is 40 msec. Each usersends a packet (including both originals and retransmissions)following a Poisson process with rate 1/400 packets/msec.

  1. (a) What is the chance of success on Alice’ first attempt?(hint: the probability that there is no othertransmission withinthe vulnerable period of Alice’s attempt)

  2. (b) What is the probability that Alice gets exactly k collisionsand then a success? (hint: consider a Bernoulli trials process)

  3. (c) What is the expected number of transmission attempts neededto successfully send a packet?

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