document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205407>Question 1205407</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that X and Y Have the following joint probability distribution\r<BR>\n" );
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document.write( "f(x,y)	x	2	4<BR>\n" );
document.write( "	1	0.10	0.15<BR>\n" );
document.write( "y	3	0.20	0.30<BR>\n" );
document.write( "	5	0.10	0.15\r<BR>\n" );
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document.write( "a. Find the marginal distribution of X.<BR>\n" );
document.write( "b. Find the marginal distribution of Y.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845485 by </B><A HREF=/tutors/aboutme.mpl?userid=moonwhisperer><B>moonwhisperer(1)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=moonwhisperer><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=moonwhisperer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=845485\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Soln : marginal of x has two values for x=2 and x=4\r<BR>\n" );
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document.write( "For x = 2, we need to find sum of all y values over x=2 <BR>\n" );
document.write( "i.e. (2,1)+(2,3)+(2,5) = 0.1 + 0.2 + 0.1 = 0.4\r<BR>\n" );
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document.write( "For For x = 4, we need to find sum of all y values over x=4 <BR>\n" );
document.write( "i.e. (4,1)+(4,3)+(4,5) = 0.15 + 0.3 + 0.15 = 0.6 \r<BR>\n" );
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document.write( "To check marginal pdf of x sum to 1 = 0.4+ 0.6 \r<BR>\n" );
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document.write( "Similarly, <BR>\n" );
document.write( "marginal of y has three values for y=1, y=3 and y=5\r<BR>\n" );
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document.write( "For y=1, we need to find sum of all x values over y=1 <BR>\n" );
document.write( "i.e. (2,1)+(4,1) = 0.1 + 0.15 = 0.25\r<BR>\n" );
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document.write( "For y=3, we need to find sum of all x values over y=3<BR>\n" );
document.write( "i.e. (2,3)+(4,3) = 0.2 + 0.3 = 0.5\r<BR>\n" );
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document.write( "For y=5, we need to find sum of all x values over y=5 <BR>\n" );
document.write( "i.e. (2,5)+(4,5) = 0.1 + 0.15 = 0.25\r<BR>\n" );
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document.write( "To check marginal pdf of y sum to 1 = 0.25+ 0.5 + 0.25 \r<BR>\n" );
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