document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1083823>Question 1083823</A>: <I><SPAN STYLE=\"word-break: break-all;\"> there are three values in a population ,(10,30,and 50) and we are interested in investigating the sampling distributtion of the sample mean (x par )for sample of size 2.                                         -How many possible distinct random sample are ther ? A ssumes sampling whit replacement .                                - find the mean and variance of this distribution                                           -Assume sampling without replacement , how many possible random samples are there now ? what is sampling distribution now ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #697875 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=697875\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> there are 3! = 6 possible distinct random samples with replacement<BR>\n" );
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document.write( "(10,10), (10,30), (10,50), (30,30), (30,50), (50,50)<BR>\n" );
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document.write( "the population mean is (10+30+50) / 3 = 30 and variance = ( (10-30)^2 + (30-30)^2 + (50-30)^2 ) / 3 = 266.6667<BR>\n" );
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document.write( "now consider our samples<BR>\n" );
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document.write( "(10,10) - the mean is 10<BR>\n" );
document.write( "(10,30) - the mean is 20<BR>\n" );
document.write( "(10,50) - the mean is 30<BR>\n" );
document.write( "(30,30) - the mean is 30<BR>\n" );
document.write( "(30,50) - the mean is 40<BR>\n" );
document.write( "(50,50) - the mean is 50<BR>\n" );
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document.write( "the mean of the sampling distribution is (10+20+30+30+40+50) / 6 = 30<BR>\n" );
document.write( "the variance of the sampling distribution is 166.6667<BR>\n" );
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document.write( "there are 2 possible distinct random samples without replacement<BR>\n" );
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document.write( "(10,30), (30,50)<BR>\n" );
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document.write( "(10,30) - the mean is 20<BR>\n" );
document.write( "(30,50) - the mean is 40<BR>\n" );
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document.write( "the mean of the sampling distribution is (20+40) / 2 = 30<BR>\n" );
document.write( "the variance of the sampling distribution is 100<BR>\n" );
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