document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1034553>Question 1034553</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that the random variable Y  has probability distribution given by: \r<BR>\n" );
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document.write( "y  p(y)  <BR>\n" );
document.write( "-2 0.11 <BR>\n" );
document.write( "0 0.32 <BR>\n" );
document.write( "3 0.57 \r<BR>\n" );
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document.write( " Find the mean, variance, and standard deviation of Y . <BR>\n" );
document.write( "&#956; Y =    <BR>\n" );
document.write( "&#963; 2 Y =    <BR>\n" );
document.write( "&#963; Y =    <BR>\n" );
document.write( " What is the probability that Y  is between &#956; Y &#8722;3&#963; Y   and &#956; Y +3&#963; Y  ? You may find it helpful to draw a probability histogram and mark &#956; Y  , &#956; Y &#8722;3&#963; Y  , and &#956; Y +3&#963; Y  . <BR>\n" );
document.write( "P(&#956; Y &#8722;3&#963; Y <Y<&#956; Y +3&#963; Y )=     </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #649444 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=649444\">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=E%28Y%29+=+mu%5BY%5D+=+-2%2A0.11+%2B+0%2A0.32+%2B+3%2A0.57++=+1.49 ALIGN=MIDDLE  ALT=\"E%28Y%29+=+mu%5BY%5D+=+-2%2A0.11+%2B+0%2A0.32+%2B+3%2A0.57++=+1.49\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28Y%5E2%29+=+%28-2%29%5E2%2A0.11+%2B+0%5E2%2A0.32+%2B+3%5E2%2A0.57++=+5.57 ALIGN=MIDDLE  ALT=\"E%28Y%5E2%29+=+%28-2%29%5E2%2A0.11+%2B+0%5E2%2A0.32+%2B+3%5E2%2A0.57++=+5.57\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sigma%29%5E2%5BY%5D+=+E%28Y%5E2%29+-++%28mu%5BY%5D%29%5E2+=+5.57+-+1.49%5E2+=+3.3499 ALIGN=MIDDLE  ALT=\"%28sigma%29%5E2%5BY%5D+=+E%28Y%5E2%29+-++%28mu%5BY%5D%29%5E2+=+5.57+-+1.49%5E2+=+3.3499\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma%5BY%5D+=+sqrt%283.3499%29+=+1.83 ALIGN=MIDDLE  ALT=\"sigma%5BY%5D+=+sqrt%283.3499%29+=+1.83\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to three significant figures<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28mu%5BY%5D+-+3%2Asigma%5BY%5D+%3C+Y+%3C+mu%5BY%5D+%2B+3%2Asigma%5BY%5D%29+=+P%28-4+%3C+Y+%3C+6.98%29+=+1 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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