document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=394859>Question 394859</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Explain whether the following statements are true or false. Give reasons.\r<BR>\n" );
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document.write( "1. E(1/X)=1/E(X) <---- E(X) represents the expected value\r<BR>\n" );
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document.write( "2. E[X-u(subscriptX)]^2 = [E(X-u(subscriptX))]^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #280488 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=280488\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%281%2FX%29=1%2FE%28X%29 ALIGN=MIDDLE  ALT=\"E%281%2FX%29=1%2FE%28X%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  FALSE.  Consider the pmf<BR>\n" );
document.write( "X      = 1      2       3<BR>\n" );
document.write( "p(x)   =0.2     0.3     0.5<BR>\n" );
document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28X%29+=+1%2A0.2+%2B+2%2A0.3++%2B3%2A0.5+=+23%2F10 ALIGN=MIDDLE  ALT=\"E%28X%29+=+1%2A0.2+%2B+2%2A0.3++%2B3%2A0.5+=+23%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%281%2FX%29+=+1%2A0.2+%2B+%281%2F2%29%2A0.3++%2B%281%2F3%29%2A0.5+=+31%2F60 ALIGN=MIDDLE  ALT=\"E%281%2FX%29+=+1%2A0.2+%2B+%281%2F2%29%2A0.3++%2B%281%2F3%29%2A0.5+=+31%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Therefore <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%281%2FX%29 ALIGN=MIDDLE  ALT=\"E%281%2FX%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2FE%28X%29 ALIGN=MIDDLE  ALT=\"1%2FE%28X%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28%28X-u%5Bx%5D%29%5E2%29+=+%28E%28X-u%5Bx%5D%29%29%5E2 ALIGN=MIDDLE  ALT=\"E%28%28X-u%5Bx%5D%29%5E2%29+=+%28E%28X-u%5Bx%5D%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. FALSE.<BR>\n" );
document.write( "The left side is Var(X), while the right side equal to 0, because <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28E%28X-u%5Bx%5D%29%29%5E2+=+%28E%28X%29+-+u%5Bx%5D%29%5E2+=+%28u%5Bx%5D+-+u%5Bx%5D%29%5E2+=+0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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