document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=390747>Question 390747</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Risk manager developed the following probability distribution for number of auto physical claims;\r<BR>\n" );
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document.write( "# of claims     Probability<BR>\n" );
document.write( "12                    .20\r<BR>\n" );
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document.write( "15                    .60\r<BR>\n" );
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document.write( "18                    .20\r<BR>\n" );
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document.write( "The mean of probability distribution is 15 claims. What is the standard deviation?\r<BR>\n" );
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document.write( "Please explain<BR>\n" );
document.write( " the process as well. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #277189 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=277189\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu+=+15 ALIGN=MIDDLE  ALT=\"mu+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" > ===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma%5E2+=+E%28X%5E2%29+-+mu%5E2 ALIGN=MIDDLE  ALT=\"sigma%5E2+=+E%28X%5E2%29+-+mu%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma%5E2+=+%2812%5E2%2A0.20+%2B+15%5E2%2A0.60+%2B+18%5E2%2A0.20%29+-+15%5E2+=+228.6+-+225+=+3.6 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.  This is the variance of the distribution.  Its square root is the standard deviation, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma+=+%283sqrt%2810%29%29%2F5+=+1.8974+ ALIGN=MIDDLE  ALT=\"sigma+=+%283sqrt%2810%29%29%2F5+=+1.8974+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to 4 decimal places.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28X%5E2%29+ ALIGN=MIDDLE  ALT=\"E%28X%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > means expectation, or the mean of the squares of the random variables. It does NOT mean the sum of squares.  After squaring each random variable value, you have to multiply each squared value with its corresponding probability.  Please read entirely the solution to the problem. </SPAN>\n" );
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