document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=440040>Question 440040</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A point is chosen at random from the interior of a right triangle with height 1 and base 1. Let Y denote the distance from the chosen point to the base of the triangle. Find the PDF and CDF of Y. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #304071 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=304071\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let Y = the distance from the chosen point to the base of the triangle.\r<BR>\n" );
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document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28Y+%3C=+y%29+=+F%5BY%5D%28y%29+=+%28%28y%2F2%29%281%2B%281-y%29%29%29%2F%281%2F2%29+=+2%2A%28y%2F2%29%282-y%29+=+2y+-+y%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "This is the cdf of Y.<BR>\n" );
document.write( "(Note that since this is a continuous density function, P(Y = y) = 0.)\r<BR>\n" );
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document.write( "To get the PDF, get the derivative:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5BY%5D%28y%29+=+2+-+2y ALIGN=MIDDLE  ALT=\"f%5BY%5D%28y%29+=+2+-+2y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5BY%5D%28y%29+=+2%281+-+y%29 ALIGN=MIDDLE  ALT=\"f%5BY%5D%28y%29+=+2%281+-+y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the pdf of Y.<BR>\n" );
document.write( " </SPAN>\n" );
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