document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1029572>Question 1029572</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A random variable x has the possible values 1, 2, and 3. E(X)=2 and E(X^2)=5. Find P(X=1), P(X=2), and P(X=3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #644555 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=644555\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since E(X) = 2, we must have P(X = 1) = P(X = 3) = p and P(X = 2) = 1-2p for some p.\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large E(X^2) = 5\">, we have <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large 1p + 4(1-2p) + 9p = 5\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large 2p + 4 = 5\">. So p = 1/2, so \r<BR>\n" );
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document.write( "P(X = 1) = 1/2<BR>\n" );
document.write( "P(X = 2) = 0<BR>\n" );
document.write( "P(X = 3) = 1/2 </SPAN>\n" );
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