document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=998529>Question 998529</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve the following question <BR>\n" );
document.write( " “A fair die is thrown at random three independent times.  Let Y be the maximum of these three outcomes, each outcome being the number shown on the face uppermost on the die.  Find the probability density function 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 #617419 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=617419\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I used EXCEL to generate all <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=216+%283%2A3%2A3%29 ALIGN=MIDDLE  ALT=\"216+%283%2A3%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible outcomes and sums.<BR>\n" );
document.write( "1	1	1	3<BR>\n" );
document.write( "1	1	2	4<BR>\n" );
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document.write( "1	2	1	4<BR>\n" );
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document.write( "1	2	3	6<BR>\n" );
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document.write( "1	2	5	8<BR>\n" );
document.write( "1	2	6	9<BR>\n" );
document.write( "1	3	1	5<BR>\n" );
document.write( "1	3	2	6<BR>\n" );
document.write( "1	3	3	7<BR>\n" );
document.write( "1	3	4	8<BR>\n" );
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document.write( "1	3	6	10<BR>\n" );
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document.write( "1	4	2	7<BR>\n" );
document.write( "1	4	3	8<BR>\n" );
document.write( "1	4	4	9<BR>\n" );
document.write( "1	4	5	10<BR>\n" );
document.write( "1	4	6	11<BR>\n" );
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document.write( "1	5	3	9<BR>\n" );
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document.write( "So then adding up the possible outcomes from 3 to 18.<BR>\n" );
document.write( "3	1<BR>\n" );
document.write( "4	3<BR>\n" );
document.write( "5	6<BR>\n" );
document.write( "6	10<BR>\n" );
document.write( "7	15<BR>\n" );
document.write( "8	21<BR>\n" );
document.write( "9	25<BR>\n" );
document.write( "10	27<BR>\n" );
document.write( "11	27<BR>\n" );
document.write( "12	25<BR>\n" );
document.write( "13	21<BR>\n" );
document.write( "14	15<BR>\n" );
document.write( "15	10<BR>\n" );
document.write( "16	6<BR>\n" );
document.write( "17	3<BR>\n" );
document.write( "18	1<BR>\n" );
document.write( "and then dividing the outcomes by the total number of outcomes,<BR>\n" );
document.write( "3	0.0046<BR>\n" );
document.write( "4	0.0139<BR>\n" );
document.write( "5	0.0278<BR>\n" );
document.write( "6	0.0463<BR>\n" );
document.write( "7	0.0694<BR>\n" );
document.write( "8	0.0972<BR>\n" );
document.write( "9	0.1157<BR>\n" );
document.write( "10	0.1250<BR>\n" );
document.write( "11	0.1250<BR>\n" );
document.write( "12	0.1157<BR>\n" );
document.write( "13	0.0972<BR>\n" );
document.write( "14	0.0694<BR>\n" );
document.write( "15	0.0463<BR>\n" );
document.write( "16	0.0278<BR>\n" );
document.write( "17	0.0139<BR>\n" );
document.write( "18	0.0046\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );