A $1$ Mbyte file is to be transmitted over a $1$ Mbps communication line that has a bit error rate of p $=106.$

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$[5$ pts$.]$ What is the probability that the entire file is transmitted without errors? Note for n large and p very small, $(1$ p$)$n $$ e$$np$.$

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$[5$ pts$.]$ The file is broken up into N equal$-$sized blocks that are transmitted separately. What is the probability that all the blocks arrive correctly without error? Does dividing the file into blocks help?

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$[10$ pts$.]$ Suppose the propagation delay is negligible, explain how Stop$-$and$-$Wait ARQ can help deliver the file in error$-$free form. On the average how long does it take to deliver the file if the ARQ transmits the entire file each time?

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$[10$ pts$.]$ Now consider breaking up the file into N blocks. $($Neglect the overhead for the header and CRC bits.$)$ On the average how long does it take to deliver the file if the ARQ transmits the blocks one at a time? Evaluate your answer for N $=80,800,$ and $8000.$

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$[5$ pts$.]$ Explain qualitatively what happens to the answer in part $($d$)$ when the overhead is taken into account.