document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1084913>Question 1084913</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Complete the PDF table below if you know that &#963;_X=1.06752.\r<BR>\n" );
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document.write( "S	a	b	c	d	e	f	g	h<BR>\n" );
document.write( "PDF	0.01	0.05	0.2	0.55		0.05		0.01<BR>\n" );
document.write( "X	1	2	3	4	5	6	7	8<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 #698978 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=698978\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can calculate the mean,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu=1%280.01%29%2B2%280.05%29%2B3%280.2%29%2B4%280.55%29%2B5e%2B6%280.05%29%2B7g%2B8%280.01%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu=5e%2B7g%2B3.29 ALIGN=MIDDLE  ALT=\"mu=5e%2B7g%2B3.29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and then calculate the variance,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=%281-mu%29%5E2%280.01%29%2B%282-mu%29%5E2%280.05%29%2B%283-mu%29%5E2%280.2%29%2B%284-mu%29%5E2%280.55%29%2B%285-mu%29%5E2%28e%29%2B%286-mu%29%5E2%280.05%29%2B%287-mu%29%5E2%28g%29%2B%288-mu%29%5E2%280.01%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and you know that,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma=sqrt%28V%29 ALIGN=MIDDLE  ALT=\"sigma=sqrt%28V%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=1.06752%5E2 ALIGN=MIDDLE  ALT=\"V=1.06752%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=1.1395989504 ALIGN=MIDDLE  ALT=\"V=1.1395989504\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-%285e%2B7g%2B3.29%29%29%5E2%280.01%29%2B%282-%285e%2B7g%2B3.29%29%29%5E2%280.05%29%2B%283-%285e%2B7g%2B3.29%29%29%5E2%280.2%29%2B%284-%285e%2B7g%29%29%5E2%280.55%29%2B%285-%285e%2B7g%29%29%5E2%28e%29%2B%286-%285e%2B7g%29%29%5E2%280.05%29%2B%287-%285e%2B7g%29%29%5E2%28g%29%2B%288-%285e%2B7g%2B3.29%29%29%5E2%280.01%29=1.1395989504 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".\r<BR>\n" );
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document.write( "And now for the easy part.<BR>\n" );
document.write( "You also know,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.01%2B0.05%2B0.2%2B0.55%2Be%2B0.05%2Bg%2B0.01=1 ALIGN=MIDDLE  ALT=\"0.01%2B0.05%2B0.2%2B0.55%2Be%2B0.05%2Bg%2B0.01=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%2Bg=0.13 ALIGN=MIDDLE  ALT=\"e%2Bg=0.13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK, so the first part leads to the equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25e%5E3%2B95e%5E2g%2B4.65e%5E2-0.14eg-1.3529e%2B49g%5E3%2B119eg%5E2-9.31g%5E2%2B7.7763g%2B1.01877=1.1395989504 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving for the intersection of those numerically,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e=0.11 ALIGN=MIDDLE  ALT=\"e=0.11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g=0.02 ALIGN=MIDDLE  ALT=\"g=0.02\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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