SOLUTION: Data files on computers have sizes measured in megabytes. When files are sent from one computer to another down a communications links, the number of errors has a Poisson distribut

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Question 1050271: Data files on computers have sizes measured in megabytes. When files are sent from one computer to another down a communications links, the number of errors has a Poisson distribution. On average, there is one error for every 10 megabytes of data.
a. Find the probability that a 3 megabyte files is transmitted
(i) without error; (ii) with 2 or more errors.
b. Show that a file which has a 95% chance of being transmitted without error is a little over half a megabyte in size.
A commercial organisation transmits 1000 megabytes of data per day.
c. State how many errors per day they will incur on average.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
a. lambda+=+%283mb%29%2A%281%2F%2810mb%29%29+=+0.3error.
(i) The pmf is p%28x%29+=+e%5E%28-lambda%29%2A%28%28lambda%29%5Ex%2F%28x%21%29%29 ====> p%280%29+=+e%5E%28-lambda%29%2A%28%28lambda%29%5E0%2F%280%21%29%29+=+e%5E%28-0.3%29+=+0.74, to two significant figures.
(ii) p%28x+%3E=+2%29+=+1-p%280%29+-+p%281%29+=+1-+e%5E%28-0.3%29+-0.3%2A+e%5E%28-0.3%29+=+0.037

b. Let s = number of megabytes transmitted.
===> lambda+=+s%2F10
===> p%28x%29+=+e%5E%28-s%2F10%29%2A%28%28s%2F10%29%5Ex%2F%28x%21%29%29
===> p%280%29+=+e%5E%28-s%2F10%29%2A%28%28s%2F10%29%5E0%2F%280%21%29%29+=+e%5E%28-s%2F10%29.
We want e%5E%28-s%2F10%29+=+0.95.
===> s = -10ln0.95 = 0.51 megabyte of files transmitted, and the statement is proved.

c. The average is lambda+=+%281000mb%29%2A%281%2F%2810mb%29%29 = 100 errors.