document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=287629>Question 287629</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Probability Density. HELP PLEASE !!!!<BR>\n" );
document.write( "A broom stick of length 1 meter is split into two substicks at a point that is uniformly distributed. Let X be the length of the shorter substick and Y be the length of the longer substick. <BR>\n" );
document.write( "Find <BR>\n" );
document.write( "(a) the density of X <BR>\n" );
document.write( "(b) the density of Y<BR>\n" );
document.write( "(c) E(X)<BR>\n" );
document.write( "(d) Var(X)<BR>\n" );
document.write( "(e) E(Y - X)2\r<BR>\n" );
document.write( "\n" );
document.write( "As no one is attempting to answer this question (that I have posted several times), can I assume it's unsolvable ?<BR>\n" );
document.write( "Someone PLEASE reply !!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #298952 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=298952\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = 1, x in [0,1],<BR>\n" );
document.write( "f(y) = 1, y in [0,1].  (Here, Y = 1 - X.)\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu+=+E%28X%29+=+int%28x%2A1%2C+dx%2C+0%2C1%29+=+int%28x%2C+dx%2C+0%2C1%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"mu+=+E%28X%29+=+int%28x%2A1%2C+dx%2C+0%2C1%29+=+int%28x%2C+dx%2C+0%2C1%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Var%28X%29+=+E%28X%5E2%29+-+mu%5E2+=+int%28x%5E2%2A1%2C+dx%2C0%2C1%29+-+1%2F4+=+int%28x%5E2%2C+dx%2C0%2C1%29+-+1%2F4%0D%0A%0D%0A=+1%2F3+-+1%2F4+=+1%2F12 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Now <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Var%28Y-X%29+=+E%28%28Y-X%29%5E2%29+-+%28E%28Y-X%29%29%5E2 ALIGN=MIDDLE  ALT=\"Var%28Y-X%29+=+E%28%28Y-X%29%5E2%29+-+%28E%28Y-X%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=Var%28Y-X%29+%2B+%28E%28Y-X%29%29%5E2=+E%28%28Y-X%29%5E2%29 ALIGN=MIDDLE  ALT=\"Var%28Y-X%29+%2B+%28E%28Y-X%29%29%5E2=+E%28%28Y-X%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "var(Y-X) = varY + varX = var(1-X) + var X = var 1  + var X + var X = 2var X = 2/12 = 1/6.<BR>\n" );
document.write( "E(Y - X) = E(Y) - E(X) = E(1 - X) - E(X) = E1  - E(X) - E(X) = 1 - 2E(X) = <BR>\n" );
document.write( "1 - 1 = 0.\r<BR>\n" );
document.write( "\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28%28Y-X%29%5E2%29+=+Var%28Y-X%29+%2B+%28E%28Y-X%29%29%5E2+=+1%2F6+%2B+0+=+1%2F6+ ALIGN=MIDDLE  ALT=\"E%28%28Y-X%29%5E2%29+=+Var%28Y-X%29+%2B+%28E%28Y-X%29%29%5E2+=+1%2F6+%2B+0+=+1%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );