document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=394836>Question 394836</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You are told that E(X)=8 and var(X)=4. What are the expected values and variances of the following expressions:\r<BR>\n" );
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document.write( "a. Y= 3X-2<BR>\n" );
document.write( "b. Y= 0.6X-4<BR>\n" );
document.write( "c. Y= X/4<BR>\n" );
document.write( "d. Y= aX+b, where a and b are constants<BR>\n" );
document.write( "e. Y= 3X^2+2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #280193 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=280193\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are told that E(X)=8 and var(X)=4. <BR>\n" );
document.write( "What are the expected values and variances of the following expressions: <BR>\n" );
document.write( "a. Y= 3X-2<BR>\n" );
document.write( "E(3X-2) = 3E(X)-2 = 3*8-2 = 22<BR>\n" );
document.write( "Var(3X-2) = (3)^2*Var(X) = 9*4 = 36<BR>\n" );
document.write( "----------------------------------<BR>\n" );
document.write( "b. Y= 0.6X-4<BR>\n" );
document.write( "E(0.6X-4) = 0.6*E(X)-4 = 0.6*8-4 = 0.8<BR>\n" );
document.write( "Var(0.6X-4) = (0.6)^2*Var(X) = 0.36*4 = 1.44<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "c. Y= X/4<BR>\n" );
document.write( "E((1/4)X) = (1/4)E(X) = 2<BR>\n" );
document.write( "Var((1/4)X) = (1/4)^2*Var(X) = 4/16 = 1/4<BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "d. Y= aX+b, where a and b are constants<BR>\n" );
document.write( "E(aX+b) = aE(x)+b = 8a+b<BR>\n" );
document.write( "Var(aX+b) = a^2*Var(X) = 4a^2<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "e. Y= 3X^2+2<BR>\n" );
document.write( "E(3X^2+2) = 3*E(X^2)+2<BR>\n" );
document.write( "Var(3X^2+2) = 9*E(X^2)<BR>\n" );
document.write( "=============================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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