document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=609899>Question 609899</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you find expected value? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #384122 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=384122\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Intuitively, expected value is the value that you \"expect\" to obtain for a trial involving a random variable (or the average value if you repeat this trial indefinitely). For example, if you have a 1/100 chance of winning $200 and a 99/100 chance of losing $5 in a bet, your expected value is\r<BR>\n" );
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document.write( "(1/100)(200) + (99/100)(-5) = -2.95\r<BR>\n" );
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document.write( "This means that you expect to lose 2.95 on average.\r<BR>\n" );
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document.write( "The expected value is defined as\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE E(x) = \sum xP(x)\">, in other words, the weighted average of the probabilities. Note that the random variable has to be numerical, e.g. P(6 on a die roll), not P(boy).\r<BR>\n" );
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