Expected value when involving intangible factors
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Rebecca and James play the following game. James pays her 1.50 for her to roll two dice. If the sum of these two dice is exactly 6, then she will pay him of 10.50 and return him the cost of 1.50 he paid her to roll the dice. Otherwise, Rebecca will keep the 1.50. At this point the expected value is easy: One just take $$frac{31}{35} times (-1.5)+frac{5}{36}times 10.5=frac{1}{6}$$
However the question now ask, if intangible factors are included in "expectation", and say that : Before betting James only has 1.50, which he needs to take a train home. If he has to walk home, the unhappiness is equivalent to losing 15 cents.
Now I am a bit confused with this addition. Should I just naively use $frac{1}{6} - 0.15$ or do I need to consider his loss as $-1.5-0.15 = -1.65$?
probability expected-value
asked Nov 16 at 17:12
ilovewt
932517
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Rebecca and James play the following game. James pays her 1.50 for her to roll two dice. If the sum of these two dice is exactly 6, then she will pay him of 10.50 and return him the cost of 1.50 he paid her to roll the dice. Otherwise, Rebecca will keep the 1.50. At this point the expected value is easy: One just take $$frac{31}{35} times (-1.5)+frac{5}{36}times 10.5=frac{1}{6}$$
However the question now ask, if intangible factors are included in "expectation", and say that : Before betting James only has 1.50, which he needs to take a train home. If he has to walk home, the unhappiness is equivalent to losing 15 cents.
Now I am a bit confused with this addition. Should I just naively use $frac{1}{6} - 0.15$ or do I need to consider his loss as $-1.5-0.15 = -1.65$?
probability expected-value
asked Nov 16 at 17:12
ilovewt
932517
The second one, since he only is unhappy if he looses his dollar-fifty. By the way it would be easier to understand your work if you stated what you were taking the expectation of. For example it would help to define $X$ as the earnings of James (not the earnings of Rebecca), and then you are computing $E[X]$. So then $X = -1.5-.15$ if James looses, and $X=10.5$ if he wins.
– Michael
Nov 16 at 17:43
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Rebecca and James play the following game. James pays her 1.50 for her to roll two dice. If the sum of these two dice is exactly 6, then she will pay him of 10.50 and return him the cost of 1.50 he paid her to roll the dice. Otherwise, Rebecca will keep the 1.50. At this point the expected value is easy: One just take $$frac{31}{35} times (-1.5)+frac{5}{36}times 10.5=frac{1}{6}$$
However the question now ask, if intangible factors are included in "expectation", and say that : Before betting James only has 1.50, which he needs to take a train home. If he has to walk home, the unhappiness is equivalent to losing 15 cents.
Now I am a bit confused with this addition. Should I just naively use $frac{1}{6} - 0.15$ or do I need to consider his loss as $-1.5-0.15 = -1.65$?
probability expected-value
asked Nov 16 at 17:12
ilovewt
932517
Rebecca and James play the following game. James pays her 1.50 for her to roll two dice. If the sum of these two dice is exactly 6, then she will pay him of 10.50 and return him the cost of 1.50 he paid her to roll the dice. Otherwise, Rebecca will keep the 1.50. At this point the expected value is easy: One just take $$frac{31}{35} times (-1.5)+frac{5}{36}times 10.5=frac{1}{6}$$
However the question now ask, if intangible factors are included in "expectation", and say that : Before betting James only has 1.50, which he needs to take a train home. If he has to walk home, the unhappiness is equivalent to losing 15 cents.
Now I am a bit confused with this addition. Should I just naively use $frac{1}{6} - 0.15$ or do I need to consider his loss as $-1.5-0.15 = -1.65$?
probability expected-value
probability expected-value
asked Nov 16 at 17:12
ilovewt
932517
asked Nov 16 at 17:12
ilovewt
932517
asked Nov 16 at 17:12
ilovewt
932517
asked Nov 16 at 17:12
ilovewt
932517
asked Nov 16 at 17:12
ilovewt
932517
932517
The second one, since he only is unhappy if he looses his dollar-fifty. By the way it would be easier to understand your work if you stated what you were taking the expectation of. For example it would help to define $X$ as the earnings of James (not the earnings of Rebecca), and then you are computing $E[X]$. So then $X = -1.5-.15$ if James looses, and $X=10.5$ if he wins.
– Michael
Nov 16 at 17:43
add a comment |
The second one, since he only is unhappy if he looses his dollar-fifty. By the way it would be easier to understand your work if you stated what you were taking the expectation of. For example it would help to define $X$ as the earnings of James (not the earnings of Rebecca), and then you are computing $E[X]$. So then $X = -1.5-.15$ if James looses, and $X=10.5$ if he wins.
– Michael
Nov 16 at 17:43
The second one, since he only is unhappy if he looses his dollar-fifty. By the way it would be easier to understand your work if you stated what you were taking the expectation of. For example it would help to define $X$ as the earnings of James (not the earnings of Rebecca), and then you are computing $E[X]$. So then $X = -1.5-.15$ if James looses, and $X=10.5$ if he wins.
– Michael
Nov 16 at 17:43
The second one, since he only is unhappy if he looses his dollar-fifty. By the way it would be easier to understand your work if you stated what you were taking the expectation of. For example it would help to define $X$ as the earnings of James (not the earnings of Rebecca), and then you are computing $E[X]$. So then $X = -1.5-.15$ if James looses, and $X=10.5$ if he wins.
– Michael
Nov 16 at 17:43
add a comment |
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The second one, since he only is unhappy if he looses his dollar-fifty. By the way it would be easier to understand your work if you stated what you were taking the expectation of. For example it would help to define $X$ as the earnings of James (not the earnings of Rebecca), and then you are computing $E[X]$. So then $X = -1.5-.15$ if James looses, and $X=10.5$ if he wins.
– Michael
Nov 16 at 17:43