document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1100379>Question 1100379</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the probability density function of the random variable X is given by  :               <BR>\n" );
document.write( "  f(x) ={&#9608;(@1/5    for2<x<7@  @0         elsewhere       )&#9508;         <BR>\n" );
document.write( "               <BR>\n" );
document.write( "	Verify that the area under the curve is 1.            <BR>\n" );
document.write( "	Find P(3<X<5), P (X < 5).<BR>\n" );
document.write( "   c) Find the expected value of the random variable X.<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #714875 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=714875\">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=1%2F5 ALIGN=MIDDLE  ALT=\"f%28x%29=1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%3Cx%3C7 ALIGN=MIDDLE  ALT=\"2%3Cx%3C7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If you integrate over all values,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=int%28f%28x%29%2Cdx%2Cx=0%2Cinfinity%29 ALIGN=MIDDLE  ALT=\"P=int%28f%28x%29%2Cdx%2Cx=0%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=P=int%28f%28x%29%2Cdx%2Cx=0%2C2%29%2Bint%28f%28x%29%2Cdx%2Cx=2%2C5%29%2Bint%28f%28x%29%2Cdx%2Cx=5%2Cinfinity%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=0%2Bint%28f%28x%29%2Cdx%2Cx=2%2C5%29%2B0 ALIGN=MIDDLE  ALT=\"P=0%2Bint%28f%28x%29%2Cdx%2Cx=2%2C5%29%2B0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=int%28f%28x%29%2Cdx%2Cx=2%2C7%29 ALIGN=MIDDLE  ALT=\"P=int%28f%28x%29%2Cdx%2Cx=2%2C7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=%281%2F5%29%287-2%29 ALIGN=MIDDLE  ALT=\"P=%281%2F5%29%287-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=%281%2F5%29%285%29 ALIGN=MIDDLE  ALT=\"P=%281%2F5%29%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=1 ALIGN=MIDDLE  ALT=\"P=1\"   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=int%28%281%2F5%29%2Cdx%2Cx=3%2C5%29 ALIGN=MIDDLE  ALT=\"P=int%28%281%2F5%29%2Cdx%2Cx=3%2C5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=%281%2F5%29%285-3%29 ALIGN=MIDDLE  ALT=\"P=%281%2F5%29%285-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=%281%2F5%29%282%29 ALIGN=MIDDLE  ALT=\"P=%281%2F5%29%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=2%2F5 ALIGN=MIDDLE  ALT=\"P=2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
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document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=int%28f%28x%29%2Cdx%2Cx=0%2C5%29 ALIGN=MIDDLE  ALT=\"P=int%28f%28x%29%2Cdx%2Cx=0%2C5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=int%28f%28x%29%2Cdx%2Cx=0%2C2%29%2Bint%28f%28x%29%2Cdx%2Cx=2%2C5%29 ALIGN=MIDDLE  ALT=\"P=int%28f%28x%29%2Cdx%2Cx=0%2C2%29%2Bint%28f%28x%29%2Cdx%2Cx=2%2C5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=0%2Bint%28f%28x%29%2Cdx%2Cx=2%2C5%29 ALIGN=MIDDLE  ALT=\"P=0%2Bint%28f%28x%29%2Cdx%2Cx=2%2C5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=int%28f%28x%29%2Cdx%2Cx=2%2C5%29 ALIGN=MIDDLE  ALT=\"P=int%28f%28x%29%2Cdx%2Cx=2%2C5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=%281%2F5%29%285-2%29 ALIGN=MIDDLE  ALT=\"P=%281%2F5%29%285-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=%281%2F5%29%283%29 ALIGN=MIDDLE  ALT=\"P=%281%2F5%29%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=3%2F5 ALIGN=MIDDLE  ALT=\"P=3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );