document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1050271>Question 1050271</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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.<BR>\n" );
document.write( "a. Find the probability that a 3 megabyte files is transmitted<BR>\n" );
document.write( "(i) without error; (ii) with 2 or more errors.<BR>\n" );
document.write( "b. Show that a file which has a 95% chance of being transmitted without error is a little over half a megabyte in size.<BR>\n" );
document.write( "A commercial organisation transmits 1000 megabytes of data per day.<BR>\n" );
document.write( "c. State how many errors per day they will incur on average.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #667038 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=667038\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lambda+=+%283mb%29%2A%281%2F%2810mb%29%29+=+0.3 ALIGN=MIDDLE  ALT=\"lambda+=+%283mb%29%2A%281%2F%2810mb%29%29+=+0.3\"   DISABLED_style= \"max-width:90%; height:auto;\" >error.\r<BR>\n" );
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document.write( "(i) The pmf is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29+=+e%5E%28-lambda%29%2A%28%28lambda%29%5Ex%2F%28x%21%29%29 ALIGN=MIDDLE  ALT=\"p%28x%29+=+e%5E%28-lambda%29%2A%28%28lambda%29%5Ex%2F%28x%21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ====> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=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 ALIGN=MIDDLE  ALT=\"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\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to two significant figures.\r<BR>\n" );
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document.write( "(ii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=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 ALIGN=MIDDLE  ALT=\"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\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b. Let s = number of megabytes transmitted.<BR>\n" );
document.write( "===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lambda+=+s%2F10 ALIGN=MIDDLE  ALT=\"lambda+=+s%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29+=+e%5E%28-s%2F10%29%2A%28%28s%2F10%29%5Ex%2F%28x%21%29%29 ALIGN=MIDDLE  ALT=\"p%28x%29+=+e%5E%28-s%2F10%29%2A%28%28s%2F10%29%5Ex%2F%28x%21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=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 ALIGN=MIDDLE  ALT=\"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\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "We want <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-s%2F10%29+=+0.95 ALIGN=MIDDLE  ALT=\"e%5E%28-s%2F10%29+=+0.95\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "===> s = -10ln0.95 = 0.51 megabyte of files transmitted, and the statement is proved.\r<BR>\n" );
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document.write( "c. The average is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lambda+=+%281000mb%29%2A%281%2F%2810mb%29%29 ALIGN=MIDDLE  ALT=\"lambda+=+%281000mb%29%2A%281%2F%2810mb%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 100 errors.<BR>\n" );
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