document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=394836>Question 394836</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You are told that E(X)=8 and var(X)=4. What are the expected values and variances of the following expressions:\r<BR>\n" );
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document.write( "a. Y= 3X-2<BR>\n" );
document.write( "b. Y= 0.6X-4<BR>\n" );
document.write( "c. Y= X/4<BR>\n" );
document.write( "d. Y= aX+b, where a and b are constants<BR>\n" );
document.write( "e. Y= 3X^2+2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #280217 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=280217\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> e. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Var+%28X%29+=+E%28X%5E2%29++-+%28E%28X%29%29%5E2 ALIGN=MIDDLE  ALT=\"Var+%28X%29+=+E%28X%5E2%29++-+%28E%28X%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+=+E%28X%5E2%29+-+8%5E2 ALIGN=MIDDLE  ALT=\"4+=+E%28X%5E2%29+-+8%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28X%5E2%29+=+68 ALIGN=MIDDLE  ALT=\"E%28X%5E2%29+=+68\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28Y%29+=+E%283X%5E2+%2B+2%29+=+3E%28X%5E2%29+%2B+2+=+3%2A68+%2B+2+=+206+ ALIGN=MIDDLE  ALT=\"E%28Y%29+=+E%283X%5E2+%2B+2%29+=+3E%28X%5E2%29+%2B+2+=+3%2A68+%2B+2+=+206+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now \r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Var+%28Y%29+=+Var%283X%5E2++%2B2%29+=+9Var+%28X%5E2%29 ALIGN=MIDDLE  ALT=\"Var+%28Y%29+=+Var%283X%5E2++%2B2%29+=+9Var+%28X%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%28E%28X%5E4%29+-+%28E%28X%5E2%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"9%28E%28X%5E4%29+-+%28E%28X%5E2%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9E%28X%5E4%29+-+9%2A68%5E2+=+9E%28X%5E4%29+-+41616 ALIGN=MIDDLE  ALT=\"9E%28X%5E4%29+-+9%2A68%5E2+=+9E%28X%5E4%29+-+41616\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Hence <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Var%283X%5E2++%2B2%29+=+9E%28X%5E4%29+-+41616 ALIGN=MIDDLE  ALT=\"Var%283X%5E2++%2B2%29+=+9E%28X%5E4%29+-+41616\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28X%5E4%29 ALIGN=MIDDLE  ALT=\"E%28X%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the 4th moment about the origin, and can't be evaluated without knowledge of the density function. </SPAN>\n" );
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