document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=604855>Question 604855</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the variance of a random variable X having the following probability distribution. The<BR>\n" );
document.write( "random variable X has expected value E(x) = .8.\r<BR>\n" );
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document.write( "x P(X = x)<BR>\n" );
document.write( "-4 - 0.3<BR>\n" );
document.write( "0 - 0.2<BR>\n" );
document.write( "4 - 0.5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #381464 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=381464\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Variance\r<BR>\n" );
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document.write( "sigma^2 = Sum( P(X = xi) * (xi - E(X) )^2 )\r<BR>\n" );
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document.write( "sigma^2 = [0.3*(-4 - 0.8)^2] + [0.2*(0 - 0.8)^2] + [0.5*(4 - 0.8)^2]\r<BR>\n" );
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document.write( "sigma^2 = [0.3*(-4.8)^2] + [0.2*(-0.8)^2] + [0.5*(3.2)^2]\r<BR>\n" );
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document.write( "sigma^2 = 0.3*23.04 + 0.2*0.64 + 0.5*10.24\r<BR>\n" );
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document.write( "sigma^2 = 6.912 + 0.128 + 5.12\r<BR>\n" );
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document.write( "sigma^2 = 12.16\r<BR>\n" );
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document.write( "So the variance is 12.16<BR>\n" );
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