#11
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Re: Econ HW - Expected Value
How about this question:
A fair coin is flipped twice and the following payoffs are assigned to each of the four possible outcomes: H-H: win 20, H-T: win 9, T-H: lose 7, T-T: lose 16. What is the expected value of this gamble? I'm thinking I know how to do this one, but I'm also thinking it's harder than I am figuring it to be. |
#12
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Re: Econ HW - Expected Value
[ QUOTE ]
(100 + P)^2 = (.25)(110)^2 + (.75)(100)^2 10000 + 200P + P*P = 10525 P^2 + 200P - 525 = 0 P = $2.59 [/ QUOTE ] I'm a freakin' idiot. How do you solve for P in that last step? |
#13
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Re: Econ HW - Expected Value
a=1
b=200 c=-525 b=(-b+/-sqrt(b^2-4ac))/(2a) |
#14
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Re: Econ HW - Expected Value
Quadratic equation. It looks like it would be a pain to factor it, but you might be able to (the second solution you get with the quadratic equation is negative and obviously doesn't apply here).
For the coin question: To calculate EV, you need to multiply two things together. 1) probability of an event happening. 2) utility when that event happens (some will be positive, some negative, in this coin problem) Do this for all the possible events in the problem and then add the products together. The coin problem should be very simple. |
#15
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Re: Econ HW - Expected Value
[ QUOTE ]
a=1 b=200 c=-525 b=(-b+/-sqrt(b^2-4ac))/(2a) [/ QUOTE ] Ok, that's what I thought. I kept thinking there had to be a different way. I'm really not as dumb as I appear! [img]/images/graemlins/blush.gif[/img] |
#16
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Re: Econ HW - Expected Value
[ QUOTE ]
Quadratic equation. It looks like it would be a pain to factor it, but you might be able to (the second solution you get with the quadratic equation is negative and obviously doesn't apply here). For the coin question: To calculate EV, you need to multiply two things together. 1) probability of an event happening. 2) utility when that event happens (some will be positive, some negative, in this coin problem) Do this for all the possible events in the problem and then add the products together. The coin problem should be very simple. [/ QUOTE ] Yeah I thought so. (.5)(.5)(20)+(.5)(.5)(9)+(.5)(.5)(-7)+(.5)(.5)(-16) = 1.5 |
#17
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Re: Econ HW - Expected Value
[ QUOTE ]
Ok, that makes sense. Maybe I'm thinking too much in probabilities? How would this relate to the EV of a flip of a coin? Could you show me that? I know it's .5, but I'd like to see how we do that too. [/ QUOTE ] EV= probability times value: the probability is .5, but there is no true value, like a dice has a set value of 1,2,3... etc. but there is no set values for a coin. If you set heads=1 and tails=0, then the EV=.5 for a fair coin, but for a normal, unspecified situation stating the EV is kinda strange... if you know what I mean. |
#18
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Re: Econ HW - Expected Value
Say we have a two-sided disc with a 1 and 2. If we flip the disc, the probability of getting a 1 or 2 is 1/2. Taking the example of the die, then the EV of flipping the disc would be 1(.5)+2(.5) = 1.5, correct?
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#19
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Re: Econ HW - Expected Value
[ QUOTE ]
Say we have a two-sided disc with a 1 and 2. If we flip the disc, the probability of getting a 1 or 2 is 1/2. Taking the example of the die, then the EV of flipping the disc would be 1(.5)+2(.5) = 1.5, correct? [/ QUOTE ] exactly. |
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