document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=503214>Question 503214</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A random variable X has mean 110 and standard deviation 18, and a random variable Y has mean 215 and standard deviation 30; and the correlation between X and Y is r=0.75. The standard deviation of X+Y is [x]. (Round your answer to 2 decimal places.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #339141 by </B><A HREF=/tutors/aboutme.mpl?userid=Sarpi><B>Sarpi(32)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Sarpi><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=Sarpi><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=339141\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> E(.)= the mean<BR>\n" );
document.write( "s(.)= the standard deviation\r<BR>\n" );
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document.write( "So, E(X)=110 s(X)=18 ; E(Y)=215 s(Y)=30<BR>\n" );
document.write( "    r(X,Y)=0.75<BR>\n" );
document.write( "The standard deviation of X+Y, formula; <BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Var%28X%2BY%29=+Var%28x%29%2BVar%28y%29%2B2cov%28x%2Cy%29 ALIGN=MIDDLE  ALT=\"Var%28X%2BY%29=+Var%28x%29%2BVar%28y%29%2B2cov%28x%2Cy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \"Var= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2 ALIGN=MIDDLE  ALT=\"s%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \"\r<BR>\n" );
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document.write( "The above formula comes from this general formula <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Var%28aX%2BbY%29=+a%5E2Var%28x%29%2Bb%5E2Var%28y%29%2B2abcov%28x%2Cy%29 ALIGN=MIDDLE  ALT=\"Var%28aX%2BbY%29=+a%5E2Var%28x%29%2Bb%5E2Var%28y%29%2B2abcov%28x%2Cy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > note: a and b are equal to 1, the coefficient of X and Y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Var%28X%2BY%29=+18%5E2%2B30%5E2%2B2cov%28x%2Cy%29 ALIGN=MIDDLE  ALT=\"Var%28X%2BY%29=+18%5E2%2B30%5E2%2B2cov%28x%2Cy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We therefore need to find the covariance of X and Y<BR>\n" );
document.write( "Formula: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28x%2Cy%29=+Cov%28x%2Cy%29%2F%28s%28x%29%2As%28y%29%29 ALIGN=MIDDLE  ALT=\"r%28x%2Cy%29=+Cov%28x%2Cy%29%2F%28s%28x%29%2As%28y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . The actual formula for finding the cov(x,y) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28XY%29-E%28X%29%2AE%28Y%29 ALIGN=MIDDLE  ALT=\"E%28XY%29-E%28X%29%2AE%28Y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We don't know the value of E(XY) so we use the alternative since r(x,y) is given.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28x%2Cy%29=+Cov%28x%2Cy%29%2F%28s%28x%29%2As%28y%29%29 ALIGN=MIDDLE  ALT=\"r%28x%2Cy%29=+Cov%28x%2Cy%29%2F%28s%28x%29%2As%28y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.75=+Cov%28x%2Cy%29%2F%2818%2A30%29 ALIGN=MIDDLE  ALT=\"0.75=+Cov%28x%2Cy%29%2F%2818%2A30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Cov%28x%2Cy%29=+0.75%2A%2818%2A30%29 ALIGN=MIDDLE  ALT=\"Cov%28x%2Cy%29=+0.75%2A%2818%2A30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cov(x,y)=405\r<BR>\n" );
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document.write( "However, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Var%28X%2BY%29=+18%5E2%2B30%5E2%2B2cov%28x%2Cy%29 ALIGN=MIDDLE  ALT=\"Var%28X%2BY%29=+18%5E2%2B30%5E2%2B2cov%28x%2Cy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "         <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Var%28X%2BY%29=+18%5E2%2B30%5E2%2B2%2A405 ALIGN=MIDDLE  ALT=\"Var%28X%2BY%29=+18%5E2%2B30%5E2%2B2%2A405\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "           <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Var%28X%2BY%29=+2034 ALIGN=MIDDLE  ALT=\"Var%28X%2BY%29=+2034\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That implies <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282034%29 ALIGN=MIDDLE  ALT=\"sqrt%282034%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equal to the standard deviation of X+Y<BR>\n" );
document.write( "So, s(X+Y)=45.10\r<BR>\n" );
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document.write( "I hope you really understand the steps. And your feedback will be appreciated. </SPAN>\n" );
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