document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=663910>Question 663910</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the variance of the following probability distribution.<BR>\n" );
document.write( "x	P(x)<BR>\n" );
document.write( "0	0.1052<BR>\n" );
document.write( "1	0.0455<BR>\n" );
document.write( "2	0.3337<BR>\n" );
document.write( "3	0.3754<BR>\n" );
document.write( "4	0.1401\r<BR>\n" );
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document.write( "variance =  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #413024 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=413024\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Mean or Expected Value:\r<BR>\n" );
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document.write( "E[X] = Sum( P(X = xi) * xi )\r<BR>\n" );
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document.write( "E[X] = [P(X = x1)*(x1)] + [P(X = x2)*(x2)] + [P(X = x3)*(x3)] + [P(X = x4)*(x4)] + [P(X = x5)*(x5)]\r<BR>\n" );
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document.write( "E[X] = [0.1052*(0)] + [0.0455*(1)] + [0.3337*(2)] + [0.3754*(3)] + [0.1401*(4)]\r<BR>\n" );
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document.write( "E[X] = 0.1052*(0) + 0.0455*(1) + 0.3337*(2) + 0.3754*(3) + 0.1401*(4)\r<BR>\n" );
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document.write( "E[X] = 0 + 0.0455 + 0.6674 + 1.1262 + 0.5604\r<BR>\n" );
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document.write( "E[X] = 2.3995\r<BR>\n" );
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document.write( "So mu = 2.3995\r<BR>\n" );
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document.write( "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 = [P(X = x1)*(x1 - mu)^2] + [P(X = x2)*(x2 - mu)^2] + [P(X = x3)*(x3 - mu)^2] + [P(X = x4)*(x4 - mu)^2] + [P(X = x5)*(x5 - mu)^2]\r<BR>\n" );
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document.write( "sigma^2 = [0.1052*(0 - 2.3995)^2] + [0.0455*(1 - 2.3995)^2] + [0.3337*(2 - 2.3995)^2] + [0.3754*(3 - 2.3995)^2] + [0.1401*(4 - 2.3995)^2]\r<BR>\n" );
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document.write( "sigma^2 = [0.1052*(-2.3995)^2] + [0.0455*(-1.3995)^2] + [0.3337*(-0.3995)^2] + [0.3754*(0.6005)^2] + [0.1401*(1.6005)^2]\r<BR>\n" );
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document.write( "sigma^2 = [0.1052*(5.75760025)] + [0.0455*(1.95860025)] + [0.3337*(0.15960025)] + [0.3754*(0.36060025)] + [0.1401*(2.56160025)]\r<BR>\n" );
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document.write( "sigma^2 = 0.1052*(5.75760025) + 0.0455*(1.95860025) + 0.3337*(0.15960025) + 0.3754*(0.36060025) + 0.1401*(2.56160025)\r<BR>\n" );
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document.write( "sigma^2 = 0.6056995463 + 0.089116311375 + 0.053258603425 + 0.13536933385 + 0.358880195025\r<BR>\n" );
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document.write( "sigma^2 = 1.242323989975\r<BR>\n" );
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document.write( "So the variance is roughly 1.242323989975 </SPAN>\n" );
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