# What is the rate at which successful packets arrive?

after traversing a wireless error filled channel packets arrive at a network node according to a Poisson process with rate λ. these packets could have corrupted bits due to the wireless channel which has a bit error probability p. A packet is said to arrive at the node successfully if no bits are in error. the number of bits in a given packet is Poisson distributed with mean μ.Assume packets are not transmitted . find the rate at which successful packets arrive at the network node

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@ mhmsa: Kindly tag it as homework if it is a homework problem. –  user17762 Nov 14 '10 at 8:35
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## 1 Answer

Calculate the probability that a (single) random packet arrives successfully. Conclude the sought rate.

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well i am not sure is it λ(1-p)^μ –  mhmsa Nov 14 '10 at 15:23
How did you calculate the probability that a packet arrives successfully? ($\mu$ is only its <i>expected</i> length) –  Yuval Filmus Nov 14 '10 at 18:15
no sorry that was wrong the answer is P(one correct Packet)=Sum(P(packet is correct of length N)*P(packet is of Length N)) the summation is over N and then multiply by λ to get the rate –  mhmsa Nov 14 '10 at 19:32
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