document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=437225>Question 437225</A>: <I><SPAN STYLE=\"word-break: break-all;\">  <BR>\n" );
document.write( "f(x)= 3x+1/k     for x= (1,3,5,7,9,11)<BR>\n" );
document.write( "        0   otherwise\r<BR>\n" );
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document.write( "a.	Find the value of k that will make this function a “true” pdf.<BR>\n" );
document.write( "b.	Find the mean, variance and standard deviation for this random variable.<BR>\n" );
document.write( "c.	Find P(x>3)<BR>\n" );
document.write( "d.	Find P(1&#8804;x&#8804;9)<BR>\n" );
document.write( "e.	Find P(x<9)<BR>\n" );
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 #302412 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=302412\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28%283x%2B1%29%2Fk%2C+x%29+=+%283%281%2B3%2B5%2B7%2B9%2B11%29+%2B+6%29%2Fk+=+%28108+%2B+6%29%2Fk+=+114%2Fk+=+1 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> k = 114.<BR>\n" );
document.write( "b.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu+=+%281%2F114%29sum%28x%283x%2B1%29%2C+x%29=%281%2F114%29%283%281%5E2+%2B+3%5E2+%2B+5%5E2+%2B+7%5E2+%2B+9%5E2+%2B+11%5E2%29+%2B+%281%2B3%2B5%2B7%2B9%2B11%29%29+=+146%2F19+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma%5E2+=+E%28X%5E2%29+-+mu%5E2+=+%281%2F114%29sum%28x%5E2%283x%2B1%29%2C+x%29+-+%28146%2F19%29%5E2 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=%281%2F114%29%283%281%5E3+%2B+3%5E3+%2B+5%5E3+%2B+7%5E3+%2B+9%5E3+%2B+11%5E3%29+%2B+%281%5E2%2B3%5E2%2B5%5E2%2B7%5E2%2B9%5E2%2B11%5E2%29%29+-+%28146%2F19%29%5E2+=+10.724838+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >, to 6 decimal places. </SPAN>\n" );
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