document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1098897>Question 1098897</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It is so long since I had my bike stolen that I am considering selling my bike lock for<BR>\n" );
document.write( "£50 and just leaving the bike unlocked. Police statistics suggest that, if a bike is left<BR>\n" );
document.write( "unlocked:<BR>\n" );
document.write( "• There is a 50% chance that it will not be stolen<BR>\n" );
document.write( "• There is a 40% chance that the wheel (worth £75) will be stolen<BR>\n" );
document.write( "• There is a 10% chance that the entire bike (worth £250) will be stolen<BR>\n" );
document.write( "I try to think about the decision in terms of probabilities:<BR>\n" );
document.write( "(a) Define a random variable X to represent this situation (i.e. define a mapping<BR>\n" );
document.write( "from events to values of X, with probabilities).<BR>\n" );
document.write( "(b) Calculate the expected value of X.<BR>\n" );
document.write( "(c) Thinking in purely economic terms, does it make sense to sell the bike lock? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #713287 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=713287\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> X---------------p(x) ---x*p(x)<BR>\n" );
document.write( "+50----------0.50------+25<BR>\n" );
document.write( "-75----------0.40=====-30<BR>\n" );
document.write( "-250---------0.10=====-25<BR>\n" );
document.write( "+25-55=-30, E(X)<BR>\n" );
document.write( "Economically, it doesn't make sense, since the expected value is negative.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );