document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=668663>Question 668663</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the mean and standard deviation of the following probability distribution:<BR>\n" );
document.write( " x<BR>\n" );
document.write( " 1<BR>\n" );
document.write( " 2<BR>\n" );
document.write( " 3<BR>\n" );
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document.write( "P(x)<BR>\n" );
document.write( " 0.1<BR>\n" );
document.write( " 0.8<BR>\n" );
document.write( " 0.1<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #415738 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=415738\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean = E[X] = x*P(x) for each x = 1*.1 + 2*.8 + 3* .1 = .1 + 1.6 + .3 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%282%29 ALIGN=MIDDLE  ALT=\"highlight%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Calculate E[X^2] in order to find Variance.  E[X^2] = 1^2 * .1 + 2^2 *.8 + 3^2 * .1 = .1 + 3.2 + .9 = 4.2\r<BR>\n" );
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document.write( "Var[X] = E[X^2] - E[X]^2 = 4.2 - 2^2 = 4.2 - 4 = .2\r<BR>\n" );
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document.write( "SD[X] = sqrt(Var[X]) = sqrt(.2) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28.4472%29 ALIGN=MIDDLE  ALT=\"highlight%28.4472%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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