document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=451067>Question 451067</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Having problems understanding Random Variable, Probability Distribution and Expected Value. Please help.\r<BR>\n" );
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document.write( "Question 1. The annual premium for a $5000 insurance policy against the theft of a painting is $150. If the (empirical) probability that the painting will be stolen during the year is.01, what is your expected return from the insurance company if you take out this insurance?\r<BR>\n" );
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document.write( "Question 2. On three rolls of a single die, you will lose $10 if a 5 turns up at least once, and you will win $7 otherwise. What is the expected value of the game? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #310213 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=310213\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Question 1. The annual premium for a $5000 insurance policy against the theft of a painting is $150. If the (empirical) probability that the painting will be stolen during the year is.01, what is your expected return from the insurance company if you take out this insurance? <BR>\n" );
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document.write( "Random \"return to you\" values: 4850, -150<BR>\n" );
document.write( "Corresponding Probabilities::: 0.01 , 0.99<BR>\n" );
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document.write( "Expected \"return to you\" = 0.01*4850 + 0.99*(-150) = -$100.00<BR>\n" );
document.write( "You can expect to lose $100 each year you have the policy.<BR>\n" );
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document.write( "Question 2. On three rolls of a single die, you will lose $10 if a 5 turns up at least once, and you will win $7 otherwise. What is the expected value of the game?<BR>\n" );
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document.write( "P(at least one 5 in three rolls) = 1 - P(no 5 in three) = 1-(5/6)^3 = 0.4213<BR>\n" );
document.write( "P(other results) = 1-0.4213 = 0.5787<BR>\n" );
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document.write( "Random game values: -10 , +7<BR>\n" );
document.write( "Probabilities: 0.4213 , 0.5787<BR>\n" );
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document.write( "Expected game value: 0.4213*(-10)+0.5787*7 = -0.16 = -16 cents<BR>\n" );
document.write( "You can except to lose 16 cents each time you play the game.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "============= </SPAN>\n" );
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