document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1168707>Question 1168707</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A random variable X has pdf f(x) = (3/4)(1-x^2) from -1 < x < 1. \r<BR>\n" );
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document.write( "1. Find the cdf\r<BR>\n" );
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document.write( "2. Find the first, second and third quartiles.\r<BR>\n" );
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document.write( "I have found that the cdf = F(x) = -(x^3)/4 + 3x/4<BR>\n" );
document.write( "by taking the integral of f(t) = (3/4)(1-t^2) from [-1,x]\r<BR>\n" );
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document.write( "From there I know I need to solve for F(x) = 0.25, F(x) = 0.5 and F(x) = 0.75.  However when I solve for those, I keep getting values outside of the interval [-1,1]. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #793308 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=793308\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Nice job. It is quite easy to make a sign error in doing this. I made several.  Your approach is just fine.\r<BR>\n" );
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document.write( "I set (3/4)m +3/4-(m^3/4)-(1/4)=0.25 for the 25th percentile.<BR>\n" );
document.write( "The first term is straightforward; the second is subtracting a -3/4, so is a +3/4<BR>\n" );
document.write( "the fourth term is (-1)^3 which is -1, then subtracted (+1) because the lower integral, then - again, 3 changes of sign.\r<BR>\n" );
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document.write( "Multiplying through by 4 and you get -m^3-1+3m+3=1<BR>\n" );
document.write( "m^3-3m-1=0<BR>\n" );
document.write( "m(q1)=-0.347<BR>\n" );
document.write( "Md m=0<BR>\n" );
document.write( "m(q3)=0.347\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-2%2C2%2C-1%2C1%2C%280.75%29%281-x%5E2%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-2%2C2%2C-1%2C1%2C%280.75%29%281-x%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-1%2C1%2C-1%2C1%2C-%28x%5E3%2F4%29%2B%283x%2F4%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-1%2C1%2C-1%2C1%2C-%28x%5E3%2F4%29%2B%283x%2F4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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