document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1166273>Question 1166273</A>: <I><SPAN STYLE=\"word-break: break-all;\"> d) The arrival rate of customers arriving at a bank counter follows a Poisson distribution with a mean rate of 4 per 10 minutes interval. Find the probability that <BR>\n" );
document.write( " i. Exactly 0 customer will arrive in 10 minutes interval<BR>\n" );
document.write( " ii. Exactly 2 customers will arrive in 10 minutes interval <BR>\n" );
document.write( "iii. At most 2 customers will arrive in 10 minutes interval<BR>\n" );
document.write( " iv. At least 3 customers will arrive in 10 minutes interval  <BR>\n" );
document.write( " (e) In a mainframe computer centre, execution time of programs follows an exponential distribution. The average execution time of the programs is 5 minutes. Find the probability that the execution time of programs is:<BR>\n" );
document.write( " i. Less than 4 minutes<BR>\n" );
document.write( " ii. More than 6 minutes  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #790764 by </B><A HREF=/tutors/aboutme.mpl?userid=themasterofcircuits><B>themasterofcircuits(27)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=themasterofcircuits><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=themasterofcircuits><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=790764\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> d.)\r<BR>\n" );
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document.write( "The Poisson distribution is as follows: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%2Cu%29=%28e%5E%28-u%29%2Au%5Ex%29%2Fx%21 ALIGN=MIDDLE  ALT=\"P%28x%2Cu%29=%28e%5E%28-u%29%2Au%5Ex%29%2Fx%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here, u is the mean, or 4 in this case.\r<BR>\n" );
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document.write( "i.) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%280%2C4%29=%28e%5E%28-4%29%2A4%5E0%29%2F0%21 ALIGN=MIDDLE  ALT=\"P%280%2C4%29=%28e%5E%28-4%29%2A4%5E0%29%2F0%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.01832\r<BR>\n" );
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document.write( "ii.) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%282%2C4%29=%28e%5E%28-4%29%2A4%5E2%29%2F2%21 ALIGN=MIDDLE  ALT=\"P%282%2C4%29=%28e%5E%28-4%29%2A4%5E2%29%2F2%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.14653\r<BR>\n" );
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document.write( "iii.) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%3C=2%29=P%28x=0%29%2BP%28x=1%29%2BP%28x=2%29 ALIGN=MIDDLE  ALT=\"P%28x%3C=2%29=P%28x=0%29%2BP%28x=1%29%2BP%28x=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%280%2C4%29%2BP%281%2C4%29%2BP%282%2C4%29 ALIGN=MIDDLE  ALT=\"P%280%2C4%29%2BP%281%2C4%29%2BP%282%2C4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%280%2C4%29=%28e%5E%28-4%29%2A4%5E0%29%2F0%21 ALIGN=MIDDLE  ALT=\"P%280%2C4%29=%28e%5E%28-4%29%2A4%5E0%29%2F0%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.01832\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%281%2C4%29=%28e%5E%28-4%29%2A4%5E1%29%2F1%21 ALIGN=MIDDLE  ALT=\"P%281%2C4%29=%28e%5E%28-4%29%2A4%5E1%29%2F1%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.07326\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%282%2C4%29=%28e%5E%28-4%29%2A4%5E2%29%2F2%21 ALIGN=MIDDLE  ALT=\"P%282%2C4%29=%28e%5E%28-4%29%2A4%5E2%29%2F2%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.14653\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%3C=2%29 ALIGN=MIDDLE  ALT=\"P%28x%3C=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.01832+0.07326+0.14653 = 0.23811\r<BR>\n" );
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document.write( "iv.) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%3E=3%29=1-P%28x%3C3%29=1-P%28x%3C=2%29 ALIGN=MIDDLE  ALT=\"P%28x%3E=3%29=1-P%28x%3C3%29=1-P%28x%3C=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-P%28x%3C=2%29 ALIGN=MIDDLE  ALT=\"1-P%28x%3C=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1-0.23811=0.76819\r<BR>\n" );
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document.write( "e.) I have done d.) for you. e.) is the same idea, except you need to use the Exponential Distribution, which is a special case of the Poisson Distribution.\r<BR>\n" );
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document.write( "The exponential distribution is given by: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%2Cu%29=%281%2Fu%29%2Ae%5E%28-x%2Fu%29 ALIGN=MIDDLE  ALT=\"P%28x%2Cu%29=%281%2Fu%29%2Ae%5E%28-x%2Fu%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The letter cutoff in the exponential is an 'x'.\r<BR>\n" );
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document.write( "Good luck!\r<BR>\n" );
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