document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1026509>Question 1026509</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dave gave a six question quiz to his Statistics students.  The students were talented, and no one scored below a 4.  Half the students scored 4, 40% scored 5, and 10% scored 6.  Compute the variance of this distribution (round answer to one decimal place).  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #641758 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=641758\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let X = random variable for the score<BR>\n" );
document.write( "PMF:<BR>\n" );
document.write( "X=x 1 2 3 4 5 6<BR>\n" );
document.write( "p(X=x) 0 0 0 0.50 0.40 0.10 <BR>\n" );
document.write( "==> E(X) = 1*0+2*0+3*0+4*0.50+ 5*0.40 +6*0.10 = 2+2+0.6 = 4.6, the mean of the distribution.\r<BR>\n" );
document.write( "\n" );
document.write( "PMF of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5E2 ALIGN=MIDDLE  ALT=\"X%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5E2+=+x%5E2 ALIGN=MIDDLE  ALT=\"X%5E2+=+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >     1     4     9     16      25     36<BR>\n" );
document.write( "p(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5E2+=+x%5E2 ALIGN=MIDDLE  ALT=\"X%5E2+=+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)  0     0     0    0.50    0.40    0.10 <BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28X%5E2%29+=+1%2A0%2B4%2A0%2B9%2A0%2B16%2A0.50%2B+25%2A0.40+%2B36%2A0.10+=+8%2B10%2B3.6+=+21.6+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
document.write( "\n" );
document.write( "==><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Var%28X%29+=+E%28X%5E2%29+-+%28E%28X%29%29%5E2+=+21.6+-+4.6%5E2+=+0.44 ALIGN=MIDDLE  ALT=\"+Var%28X%29+=+E%28X%5E2%29+-+%28E%28X%29%29%5E2+=+21.6+-+4.6%5E2+=+0.44\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );