document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=316278>Question 316278</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Struggling with expectation, can you help?\r<BR>\n" );
document.write( "\n" );
document.write( "The number of failures of a computer system in a week of operation has the following pmf:<BR>\n" );
document.write( " <BR>\n" );
document.write( "No of failures<BR>\n" );
document.write( "0<BR>\n" );
document.write( "1<BR>\n" );
document.write( "2<BR>\n" );
document.write( "3<BR>\n" );
document.write( "4<BR>\n" );
document.write( "5<BR>\n" );
document.write( "6<BR>\n" );
document.write( "Probability<BR>\n" );
document.write( "0.18<BR>\n" );
document.write( "0.28<BR>\n" );
document.write( "0.25<BR>\n" );
document.write( "0.18<BR>\n" );
document.write( "0.06<BR>\n" );
document.write( "0.04<BR>\n" );
document.write( "0.01<BR>\n" );
document.write( " <BR>\n" );
document.write( "(a)    Find the expected number of failures in a week.<BR>\n" );
document.write( "(b)   Find the variance of the number of failures in a week.<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #226211 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=226211\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=EV=sum%28x%2AP%28x%29%2C1%2C7%29=0%280.18%29%2B1%280.28%29%2B2%280.25%29%2B3%280.18%29%2B4%280.06%29%2B5%280.04%29%2B6%280.01%29=1.82 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=VAR=%28sigma%29%5E2=sum%28%28x-mu%29%5E2%2AP%28x%29%2C1%2C7%29=1.9076 ALIGN=MIDDLE  ALT=\"VAR=%28sigma%29%5E2=sum%28%28x-mu%29%5E2%2AP%28x%29%2C1%2C7%29=1.9076\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "where <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu ALIGN=MIDDLE  ALT=\"mu\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the average x value.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );