document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=364984>Question 364984</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Finding the mean and standard deviation. Let the random variable x represent the number of girls in a family of four children. Construct a table describing the probability distribution, then find the mean and standard deviation </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #260220 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=260220\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E4=16 ALIGN=MIDDLE  ALT=\"2%5E4=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible outcomes.<BR>\n" );
document.write( "Count the number of girls for each possible outcome.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=GGBB=2 ALIGN=MIDDLE  ALT=\"GGBB=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=GGGG=4 ALIGN=MIDDLE  ALT=\"GGGG=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The number of girls range from 0 to 4. <BR>\n" );
document.write( "Count the occurences divided by total number of outcomes to get probability.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+ ALIGN=MIDDLE  ALT=\"X+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P%28X%29 ALIGN=MIDDLE  ALT=\"+P%28X%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F16 ALIGN=MIDDLE  ALT=\"+1%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%2F16 ALIGN=MIDDLE  ALT=\"+4%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6%2F16 ALIGN=MIDDLE  ALT=\"+6%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%2F16 ALIGN=MIDDLE  ALT=\"+4%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F16 ALIGN=MIDDLE  ALT=\"+1%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Mean<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu=sum%28X%2AP%28X%29%2CX=1%2C4%29=0%281%2F16%29%2B1%284%2F16%29%2B2%286%2F16%29%2B3%284%2F16%29%2B4%281%2F16%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=sum%28X%2AP%28X%29%2CX=1%2C4%29=4%2B12%2B12%2B4%29%2F16 ALIGN=MIDDLE  ALT=\"mu=sum%28X%2AP%28X%29%2CX=1%2C4%29=4%2B12%2B12%2B4%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu=sum%28X%2AP%28X%29%2CX=1%2C4%29=32%2F16 ALIGN=MIDDLE  ALT=\"mu=sum%28X%2AP%28X%29%2CX=1%2C4%29=32%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Standard deviation (find variance first)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=VAR=sum%28%28X-mu%29%5E2%2AP%28X%29%2CX=1%2C4%29=%280-2%29%5E2%281%2F16%29%2B%281-2%29%5E2%284%2F16%29%2B%282-2%29%5E2%286%2F16%29%2B%283-2%29%5E2%284%2F16%29%2B%284-2%29%5E2%281%2F16%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=VAR=sum%28%28X-mu%29%5E2%2AP%28X%29%2CX=1%2C4%29=%284%2B4%2B0%2B4%2B4%29%2F16 ALIGN=MIDDLE  ALT=\"VAR=sum%28%28X-mu%29%5E2%2AP%28X%29%2CX=1%2C4%29=%284%2B4%2B0%2B4%2B4%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );