document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1029370>Question 1029370</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The cumulative distribution function of the random variable X is given by: <BR>\n" );
document.write( " F(x)={(1- 9/x^2 ) for( 3 < x )otherwise0<BR>\n" );
document.write( " Find the probability density function for the random variable X.<BR>\n" );
document.write( " compute p(X&#8804; 5) and p( 8< X )<BR>\n" );
document.write( " Find the expected value for the random variable X. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #644426 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=644426\">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=f%28x%29=dF%2Fdx=18%2Fx%5E3 ALIGN=MIDDLE  ALT=\"f%28x%29=dF%2Fdx=18%2Fx%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E3 ALIGN=MIDDLE  ALT=\"x%3E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=0 ALIGN=MIDDLE  ALT=\"f%28x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=3 ALIGN=MIDDLE  ALT=\"x%3C=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%3C=5%29=int%28%2818%2Fx%5E3%29%2Cdx%2C3%2C5%29=F%285%29-F%283%29=1-9%2F25-0=16%2F25 ALIGN=MIDDLE  ALT=\"p%28x%3C=5%29=int%28%2818%2Fx%5E3%29%2Cdx%2C3%2C5%29=F%285%29-F%283%29=1-9%2F25-0=16%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%3C=8%29=F%288%29-F%283%29=1-9%2F64-0=55%2F64 ALIGN=MIDDLE  ALT=\"p%28x%3C=8%29=F%288%29-F%283%29=1-9%2F64-0=55%2F64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E=int%28%28x%2Af%28x%29%29%2Cdx%2C3%2Cinfinity%29 ALIGN=MIDDLE  ALT=\"E=int%28%28x%2Af%28x%29%29%2Cdx%2C3%2Cinfinity%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E=int%28%2818%2Fx%5E2%29%2Cdx%2C3%2Cinfinity%29 ALIGN=MIDDLE  ALT=\"E=int%28%2818%2Fx%5E2%29%2Cdx%2C3%2Cinfinity%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E=-18%2Fx%2BC ALIGN=MIDDLE  ALT=\"E=-18%2Fx%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E=0-%28-18%2F3%29 ALIGN=MIDDLE  ALT=\"E=0-%28-18%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E=6 ALIGN=MIDDLE  ALT=\"E=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );