document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=440589>Question 440589</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let \"x bar\" be the sample mean for a random sample of 12 observations from a uniform (0,1). What is the mean and variance of \"x bar\"? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #304330 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=304330\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu+=+int%28x%2Af%28x%29%2C+dx%2C+a%2C+b%29+=+int%28x%2A1%2C+dx%2C+0%2C1%29+=+%28x%5E2%2F2%29%5B0%5D%5E1+=+1%2F2+-+0+=+1%2F2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28sum%28x%5Bk%5D%2C+k+=+1%2C+12%29%2F12%29+=+%281%2F12%29sum%28E%28x%5Bk%5D%29%2C+k+=+1%2C+12%29+%0D%0A%0D%0A%0D%0A=+%281%2F12%29sum%281%2F2%2C+k+=+1%2C+12%29++=+%281%2F12%29%2A6+=+1%2F2+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > is the mean of sample means of size 12.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28X%5E2%29=+int%28x%5E2%2Af%28x%29%2C+dx%2C+a%2C+b%29+=+int%28x%5E2%2A1%2C+dx%2C+0%2C1%29+=+%28x%5E3%2F3%29%5B0%5D%5E1+=+1%2F3+-+0+=+1%2F3 ALIGN=MIDDLE   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+=+1%2F3+-+1%2F4+=+1%2F12 ALIGN=MIDDLE  ALT=\"Var%28X%29+=+E%28X%5E2%29+-+mu%5E2+=+1%2F3+-+1%2F4+=+1%2F12\"   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%28sum%28x%5Bk%5D%2C+k+=+1%2C+12%29%2F12%29+=+%281%2F144%29sum%28Var%28X%5Bk%5D%29%2C+k+=+1%2C+12%29%0D%0A%0D%0A%0D%0A=+%281%2F144%29sum%281%2F12%2C+k+=+1%2C+12%29++=+%281%2F144%29%2A1+=+1%2F144+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >,assuming i.i.d. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );