document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132397>Question 1132397</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose a discrete random variable X has a probability density function given by:<BR>\n" );
document.write( "x	3	5	7	8	9	10	12	16<BR>\n" );
document.write( "P(X=x)	0.08	0.10	0.16	0.25	0.20	0.03	0.13	0.05\r<BR>\n" );
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document.write( "(Note: The probabilities add to one. Any value x which is not in the table has probability zero.)<BR>\n" );
document.write( "a)	Calculate P(X > 9)<BR>\n" );
document.write( "b)	Calculate P(X is bigger than or equal to 9)<BR>\n" );
document.write( "c)	Calculate P(5 < X is smaller than or equal to 10)<BR>\n" );
document.write( "d)	Calculate the expected value of X, E(X)<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 #749602 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=749602\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P(x>9) includes the last 3, and their sum is 0.21<BR>\n" );
document.write( "P(x>=9) includes the last 4, and that sum is 0.41<BR>\n" );
document.write( "P(5<x<=10) includes 6-10, or the middle four.  The sum is 0.64<BR>\n" );
document.write( "E(X)=sum of <BR>\n" );
document.write( "3(0.08)=0.24<BR>\n" );
document.write( "5(0.10)=0.50<BR>\n" );
document.write( "7(0.16)=1.12<BR>\n" );
document.write( "8(0.25)=2<BR>\n" );
document.write( "9(0.20)=1.8<BR>\n" );
document.write( "10(0.03)=0.3<BR>\n" );
document.write( "12(0.13)=0.156<BR>\n" );
document.write( "16(0.05)=0.8<BR>\n" );
document.write( "That sum is 6.916<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );