document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178033>Question 1178033</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A surveyor wishes to lay out a square region with each side having length 10 Units. However, because of a measurement error, he instead lays out a rectangle in which the north  -  south sides both have length X and the east  -  west sides both have length Y. Suppose that X and Y are independent and that each is uniformly distributed on the interval [8, 12]. What is the expected area of the resulting rectangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813754 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=813754\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The prob'y density function of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X ALIGN=MIDDLE  ALT=\"X\"   DISABLED_style= \"max-width:90%; height:auto;\" > (or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y ALIGN=MIDDLE  ALT=\"Y\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+1%2F4 ALIGN=MIDDLE  ALT=\"f%28x%29+=+1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, being distributed uniformly.\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28X%29+=+%281%2F4%29%2A%28int%28x%2Cdx%2C8%2C12%29+%29=+10 ALIGN=MIDDLE  ALT=\"E%28X%29+=+%281%2F4%29%2A%28int%28x%2Cdx%2C8%2C12%29+%29=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Similarly, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28Y%29+=+10 ALIGN=MIDDLE  ALT=\"E%28Y%29+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Y being identical distributionally to X.\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28A%29+=+E%28XY%29+=+E%28X%29%2AE%28Y%29+=+10%2A10+=+100 ALIGN=MIDDLE  ALT=\"E%28A%29+=+E%28XY%29+=+E%28X%29%2AE%28Y%29+=+10%2A10+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" >, since X and Y are independent random variables. </SPAN>\n" );
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